LMFDB - Embedded newform 135.2.q.a.122.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			122.3
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66533 - 1.16608i) q^{2} +(-1.43658 + 0.967587i) q^{3} +(0.729546 + 2.00441i) q^{4} +(-1.48319 - 1.67336i) q^{5} +(3.52066 + 0.0638164i) q^{6} +(1.13512 + 2.43427i) q^{7} +(0.0700073 - 0.261271i) q^{8} +(1.12755 - 2.78004i) q^{9} +O(q^{10})$	\(q+(-1.66533 - 1.16608i) q^{2} +(-1.43658 + 0.967587i) q^{3} +(0.729546 + 2.00441i) q^{4} +(-1.48319 - 1.67336i) q^{5} +(3.52066 + 0.0638164i) q^{6} +(1.13512 + 2.43427i) q^{7} +(0.0700073 - 0.261271i) q^{8} +(1.12755 - 2.78004i) q^{9} +(0.518731 + 4.51621i) q^{10} +(4.08386 + 4.86695i) q^{11} +(-2.98750 - 2.17361i) q^{12} +(1.19516 + 1.70687i) q^{13} +(0.948196 - 5.37749i) q^{14} +(3.74985 + 0.968813i) q^{15} +(2.84677 - 2.38873i) q^{16} +(-0.174154 - 0.649952i) q^{17} +(-5.11948 + 3.31487i) q^{18} +(-2.70632 + 1.56249i) q^{19} +(2.27205 - 4.19372i) q^{20} +(-3.98606 - 2.39871i) q^{21} +(-1.12573 - 12.8672i) q^{22} +(-0.409999 - 0.191186i) q^{23} +(0.152231 + 0.443076i) q^{24} +(-0.600292 + 4.96383i) q^{25} -4.23615i q^{26} +(1.07011 + 5.08477i) q^{27} +(-4.05115 + 4.05115i) q^{28} +(1.39473 + 7.90988i) q^{29} +(-5.11503 - 5.98600i) q^{30} +(-1.53858 + 0.559998i) q^{31} +(-8.06517 + 0.705611i) q^{32} +(-10.5760 - 3.04030i) q^{33} +(-0.467869 + 1.28546i) q^{34} +(2.38982 - 5.50995i) q^{35} +(6.39494 + 0.231909i) q^{36} +(2.76163 - 0.739977i) q^{37} +(6.32889 + 0.553706i) q^{38} +(-3.36850 - 1.29564i) q^{39} +(-0.541035 + 0.270367i) q^{40} +(-9.28604 - 1.63738i) q^{41} +(3.84102 + 8.64268i) q^{42} +(0.307907 - 3.51939i) q^{43} +(-6.77601 + 11.7364i) q^{44} +(-6.32439 + 2.23653i) q^{45} +(0.459846 + 0.796477i) q^{46} +(5.68707 - 2.65193i) q^{47} +(-1.77833 + 6.18611i) q^{48} +(-0.137652 + 0.164047i) q^{49} +(6.78789 - 7.56643i) q^{50} +(0.879072 + 0.765202i) q^{51} +(-2.54934 + 3.64084i) q^{52} +(5.99520 + 5.99520i) q^{53} +(4.14714 - 9.71563i) q^{54} +(2.08704 - 14.0524i) q^{55} +(0.715470 - 0.126157i) q^{56} +(2.37601 - 4.86325i) q^{57} +(6.90084 - 14.7989i) q^{58} +(6.07856 + 5.10051i) q^{59} +(0.793791 + 8.22304i) q^{60} +(-1.53937 - 0.560286i) q^{61} +(3.21525 + 0.861522i) q^{62} +(8.04727 - 0.410911i) q^{63} +(7.81729 + 4.51332i) q^{64} +(1.08356 - 4.53156i) q^{65} +(14.0673 + 17.3955i) q^{66} +(4.38163 - 3.06805i) q^{67} +(1.17572 - 0.823246i) q^{68} +(0.773987 - 0.122055i) q^{69} +(-10.4048 + 6.38916i) q^{70} +(2.05039 + 1.18380i) q^{71} +(-0.647407 - 0.489220i) q^{72} +(-1.33738 - 0.358350i) q^{73} +(-5.46189 - 1.98796i) q^{74} +(-3.94057 - 7.71180i) q^{75} +(-5.10626 - 4.28466i) q^{76} +(-7.21181 + 15.4658i) q^{77} +(4.09885 + 6.08559i) q^{78} +(-6.73243 + 1.18711i) q^{79} +(-8.21952 - 1.22075i) q^{80} +(-6.45726 - 6.26928i) q^{81} +(13.5550 + 13.5550i) q^{82} +(-2.27065 + 3.24283i) q^{83} +(1.89998 - 9.73966i) q^{84} +(-0.829302 + 1.25543i) q^{85} +(-4.61664 + 5.50190i) q^{86} +(-9.65714 - 10.0137i) q^{87} +(1.55749 - 0.726271i) q^{88} +(0.428822 + 0.742742i) q^{89} +(13.1401 + 3.65017i) q^{90} +(-2.79833 + 4.84685i) q^{91} +(0.0841016 - 0.961286i) q^{92} +(1.66846 - 2.29320i) q^{93} +(-12.5632 - 2.21523i) q^{94} +(6.62860 + 2.21118i) q^{95} +(10.9036 - 8.81742i) q^{96} +(-3.88639 - 0.340015i) q^{97} +(0.420527 - 0.112680i) q^{98} +(18.1351 - 5.86555i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.66533	−	1.16608i	−1.17756	−	0.824540i	−0.190005	−	0.981783i	$-0.560850\pi$
$2$	−1.66533	−	1.16608i	−1.17756	−	0.824540i	−0.987560	+	0.157243i	$0.949739\pi$
$3$	−1.43658	+	0.967587i	−0.829413	+	0.558637i
$3$	−1.43658	+	0.967587i	−0.829413	+	0.558637i
$4$	0.729546	+	2.00441i	0.364773	+	1.00221i
$5$	−1.48319	−	1.67336i	−0.663303	−	0.748351i
$5$	−1.48319	−	1.67336i	−0.663303	−	0.748351i
$6$	3.52066	+	0.0638164i	1.43731	+	0.0260529i
$7$	1.13512	+	2.43427i	0.429034	+	0.920067i	0.995390	+	0.0959060i	$0.0305748\pi$
$7$	1.13512	+	2.43427i	0.429034	+	0.920067i	−0.566356	+	0.824160i	$0.691647\pi$
$8$	0.0700073	−	0.261271i	0.0247513	−	0.0923732i
$9$	1.12755	−	2.78004i	0.375850	−	0.926680i
$10$	0.518731	+	4.51621i	0.164037	+	1.42815i
$11$	4.08386	+	4.86695i	1.23133	+	1.46744i	0.835842	+	0.548970i	$0.184980\pi$
$11$	4.08386	+	4.86695i	1.23133	+	1.46744i	0.395488	+	0.918471i	$0.370576\pi$
$12$	−2.98750	−	2.17361i	−0.862416	−	0.627466i
$13$	1.19516	+	1.70687i	0.331479	+	0.473401i	0.949948	−	0.312408i	$-0.101136\pi$
$13$	1.19516	+	1.70687i	0.331479	+	0.473401i	−0.618469	+	0.785809i	$0.712247\pi$
$14$	0.948196	−	5.37749i	0.253416	−	1.43719i
$15$	3.74985	+	0.968813i	0.968208	+	0.250146i
$16$	2.84677	−	2.38873i	0.711694	−	0.597182i
$17$	−0.174154	−	0.649952i	−0.0422386	−	0.157637i	0.941585	−	0.336774i	$-0.109336\pi$
$17$	−0.174154	−	0.649952i	−0.0422386	−	0.157637i	−0.983824	+	0.179138i	$0.942669\pi$
$18$	−5.11948	+	3.31487i	−1.20667	+	0.781322i
$19$	−2.70632	+	1.56249i	−0.620871	+	0.358460i	−0.777208	−	0.629243i	$-0.783365\pi$
$19$	−2.70632	+	1.56249i	−0.620871	+	0.358460i	0.156337	+	0.987704i	$0.450031\pi$
$20$	2.27205	−	4.19372i	0.508046	−	0.937744i
$21$	−3.98606	−	2.39871i	−0.869829	−	0.523441i
$22$	−1.12573	−	12.8672i	−0.240007	−	2.74329i
$23$	−0.409999	−	0.191186i	−0.0854907	−	0.0398650i	0.379403	−	0.925232i	$-0.376130\pi$
$23$	−0.409999	−	0.191186i	−0.0854907	−	0.0398650i	−0.464893	+	0.885367i	$0.653907\pi$
$24$	0.152231	+	0.443076i	0.0310740	+	0.0904425i
$25$	−0.600292	+	4.96383i	−0.120058	+	0.992767i
$26$		−	4.23615i		−	0.830778i
$27$	1.07011	+	5.08477i	0.205942	+	0.978564i
$28$	−4.05115	+	4.05115i	−0.765596	+	0.765596i
$29$	1.39473	+	7.90988i	0.258994	+	1.46883i	0.785608	+	0.618724i	$0.212350\pi$
$29$	1.39473	+	7.90988i	0.258994	+	1.46883i	−0.526614	+	0.850104i	$0.676539\pi$
$30$	−5.11503	−	5.98600i	−0.933872	−	1.09289i
$31$	−1.53858	+	0.559998i	−0.276338	+	0.100579i	−0.476472	−	0.879190i	$-0.658084\pi$
$31$	−1.53858	+	0.559998i	−0.276338	+	0.100579i	0.200134	+	0.979769i	$0.435862\pi$
$32$	−8.06517	+	0.705611i	−1.42573	+	0.124735i
$33$	−10.5760	−	3.04030i	−1.84105	−	0.529249i
$34$	−0.467869	+	1.28546i	−0.0802389	+	0.220455i
$35$	2.38982	−	5.50995i	0.403953	−	0.931351i
$36$	6.39494	+	0.231909i	1.06582	+	0.0386515i
$37$	2.76163	−	0.739977i	0.454009	−	0.121651i	−0.0245656	−	0.999698i	$-0.507820\pi$
$37$	2.76163	−	0.739977i	0.454009	−	0.121651i	0.478575	+	0.878047i	$0.341154\pi$
$38$	6.32889	+	0.553706i	1.02668	+	0.0898230i
$39$	−3.36850	−	1.29564i	−0.539392	−	0.207468i
$40$	−0.541035	+	0.270367i	−0.0855452	+	0.0427487i
$41$	−9.28604	−	1.63738i	−1.45024	−	0.255716i	−0.607618	−	0.794229i	$-0.707875\pi$
$41$	−9.28604	−	1.63738i	−1.45024	−	0.255716i	−0.842617	+	0.538514i	$0.818986\pi$
$42$	3.84102	+	8.64268i	0.592682	+	1.33359i
$43$	0.307907	−	3.51939i	0.0469554	−	0.536702i	−0.935893	−	0.352285i	$-0.885405\pi$
$43$	0.307907	−	3.51939i	0.0469554	−	0.536702i	0.982848	−	0.184417i	$-0.0590397\pi$
$44$	−6.77601	+	11.7364i	−1.02152	+	1.76933i
$45$	−6.32439	+	2.23653i	−0.942785	+	0.333402i
$46$	0.459846	+	0.796477i	0.0678006	+	0.117434i
$47$	5.68707	−	2.65193i	0.829545	−	0.386823i	0.0390089	−	0.999239i	$-0.487580\pi$
$47$	5.68707	−	2.65193i	0.829545	−	0.386823i	0.790536	+	0.612416i	$0.209802\pi$
$48$	−1.77833	+	6.18611i	−0.256680	+	0.892888i
$49$	−0.137652	+	0.164047i	−0.0196646	+	0.0234353i
$50$	6.78789	−	7.56643i	0.959952	−	1.07005i
$51$	0.879072	+	0.765202i	0.123095	+	0.107150i
$52$	−2.54934	+	3.64084i	−0.353530	+	0.504894i
$53$	5.99520	+	5.99520i	0.823504	+	0.823504i	0.986609	−	0.163105i	$-0.0521508\pi$
$53$	5.99520	+	5.99520i	0.823504	+	0.823504i	−0.163105	+	0.986609i	$0.552151\pi$
$54$	4.14714	−	9.71563i	0.564355	−	1.32213i
$55$	2.08704	−	14.0524i	0.281417	−	1.89483i
$56$	0.715470	−	0.126157i	0.0956087	−	0.0168584i
$57$	2.37601	−	4.86325i	0.314710	−	0.644153i
$58$	6.90084	−	14.7989i	0.906125	−	1.94319i
$59$	6.07856	+	5.10051i	0.791361	+	0.664030i	0.946082	−	0.323928i	$-0.105003\pi$
$59$	6.07856	+	5.10051i	0.791361	+	0.664030i	−0.154721	+	0.987958i	$0.549448\pi$
$60$	0.793791	+	8.22304i	0.102478	+	1.06159i
$61$	−1.53937	−	0.560286i	−0.197096	−	0.0717372i	0.241586	−	0.970379i	$-0.422332\pi$
$61$	−1.53937	−	0.560286i	−0.197096	−	0.0717372i	−0.438682	+	0.898642i	$0.644555\pi$
$62$	3.21525	+	0.861522i	0.408337	+	0.109413i
$63$	8.04727	−	0.410911i	1.01386	−	0.0517700i
$64$	7.81729	+	4.51332i	0.977162	+	0.564165i
$65$	1.08356	−	4.53156i	0.134399	−	0.562071i
$66$	14.0673	+	17.3955i	1.73157	+	2.14124i
$67$	4.38163	−	3.06805i	0.535302	−	0.374822i	−0.274444	−	0.961603i	$-0.588494\pi$
$67$	4.38163	−	3.06805i	0.535302	−	0.374822i	0.809746	+	0.586781i	$0.199605\pi$
$68$	1.17572	−	0.823246i	0.142577	−	0.0998333i
$69$	0.773987	−	0.122055i	0.0931771	−	0.0146937i
$70$	−10.4048	+	6.38916i	−1.24362	+	0.763651i
$71$	2.05039	+	1.18380i	0.243337	+	0.140491i	0.616710	−	0.787191i	$-0.288465\pi$
$71$	2.05039	+	1.18380i	0.243337	+	0.140491i	−0.373372	+	0.927682i	$0.621799\pi$
$72$	−0.647407	−	0.489220i	−0.0762976	−	0.0576551i
$73$	−1.33738	−	0.358350i	−0.156529	−	0.0419417i	0.179704	−	0.983721i	$-0.442486\pi$
$73$	−1.33738	−	0.358350i	−0.156529	−	0.0419417i	−0.336232	+	0.941779i	$0.609153\pi$
$74$	−5.46189	−	1.98796i	−0.634932	−	0.231096i
$75$	−3.94057	−	7.71180i	−0.455018	−	0.890482i
$76$	−5.10626	−	4.28466i	−0.585728	−	0.491484i
$77$	−7.21181	+	15.4658i	−0.821861	+	1.76249i
$78$	4.09885	+	6.08559i	0.464103	+	0.689058i
$79$	−6.73243	+	1.18711i	−0.757458	+	0.133560i	−0.539023	−	0.842291i	$-0.681206\pi$
$79$	−6.73243	+	1.18711i	−0.757458	+	0.133560i	−0.218435	+	0.975851i	$0.570095\pi$
$80$	−8.21952	−	1.22075i	−0.918970	−	0.136484i
$81$	−6.45726	−	6.26928i	−0.717473	−	0.696586i
$82$	13.5550	+	13.5550i	1.49690	+	1.49690i
$83$	−2.27065	+	3.24283i	−0.249236	+	0.355946i	−0.924203	−	0.381902i	$-0.875269\pi$
$83$	−2.27065	+	3.24283i	−0.249236	+	0.355946i	0.674966	+	0.737848i	$0.264158\pi$
$84$	1.89998	−	9.73966i	0.207305	−	1.06268i
$85$	−0.829302	+	1.25543i	−0.0899505	+	0.136170i
$86$	−4.61664	+	5.50190i	−0.497825	+	0.593285i
$87$	−9.65714	−	10.0137i	−1.03535	−	1.07358i
$88$	1.55749	−	0.726271i	0.166029	−	0.0774208i
$89$	0.428822	+	0.742742i	0.0454551	+	0.0787305i	0.887858	−	0.460118i	$-0.152193\pi$
$89$	0.428822	+	0.742742i	0.0454551	+	0.0787305i	−0.842403	+	0.538848i	$0.818860\pi$
$90$	13.1401	+	3.65017i	1.38509	+	0.384761i
$91$	−2.79833	+	4.84685i	−0.293345	+	0.508088i
$92$	0.0841016	−	0.961286i	0.00876820	−	0.100221i
$93$	1.66846	−	2.29320i	0.173011	−	0.237794i
$94$	−12.5632	−	2.21523i	−1.29579	−	0.228483i
$95$	6.62860	+	2.21118i	0.680080	+	0.226862i
$96$	10.9036	−	8.81742i	1.11284	−	0.899924i
$97$	−3.88639	−	0.340015i	−0.394603	−	0.0345233i	−0.111872	−	0.993723i	$-0.535685\pi$
$97$	−3.88639	−	0.340015i	−0.394603	−	0.0345233i	−0.282731	+	0.959199i	$0.591240\pi$
$98$	0.420527	−	0.112680i	0.0424797	−	0.0113824i
$99$	18.1351	−	5.86555i	1.82264	−	0.589510i
$100$	−10.3875	+	2.41811i	−1.03875	+	0.241811i
$101$	4.66297	−	12.8114i	0.463983	−	1.27478i	−0.458482	−	0.888704i	$-0.651607\pi$
$101$	4.66297	−	12.8114i	0.463983	−	1.27478i	0.922465	−	0.386080i	$-0.126171\pi$
$102$	−0.571661	−	2.29938i	−0.0566028	−	0.227672i
$103$	6.33428	−	0.554178i	0.624135	−	0.0546047i	0.229299	−	0.973356i	$-0.426357\pi$
$103$	6.33428	−	0.554178i	0.624135	−	0.0546047i	0.394837	+	0.918751i	$0.370801\pi$
$104$	0.529626	−	0.192768i	0.0519341	−	0.0189025i
$105$	1.89817	+	10.2279i	0.185243	+	0.998137i
$106$	−2.99312	−	16.9748i	−0.290718	−	1.64874i
$107$	−7.42914	+	7.42914i	−0.718202	+	0.718202i	−0.968237	−	0.250035i	$-0.919558\pi$
$107$	−7.42914	+	7.42914i	−0.718202	+	0.718202i	0.250035	+	0.968237i	$0.419558\pi$
$108$	−9.41127	+	5.85451i	−0.905600	+	0.563350i
$109$			2.73749i			0.262204i	0.991369	+	0.131102i	$0.0418515\pi$
$109$			2.73749i			0.262204i	−0.991369	+	0.131102i	$0.958148\pi$
$110$	−19.8618	+	20.9682i	−1.89374	+	1.99924i
$111$	−3.25132	+	3.73516i	−0.308602	+	0.354525i
$112$	9.04622	+	4.21832i	0.854788	+	0.398594i
$113$	−1.76514	−	20.1756i	−0.166050	−	1.89796i	−0.386073	−	0.922468i	$-0.626169\pi$
$113$	−1.76514	−	20.1756i	−0.166050	−	1.89796i	0.220022	−	0.975495i	$-0.429387\pi$
$114$	−9.62774	+	5.32830i	−0.901721	+	0.499041i
$115$	0.288184	+	0.969643i	0.0268733	+	0.0904197i
$116$	−14.8371	+	8.56623i	−1.37759	+	0.795354i
$117$	6.09278	−	1.39802i	0.563278	−	0.129247i
$118$	−4.17521	−	15.5821i	−0.384359	−	1.43445i
$119$	1.38447	−	1.16171i	0.126914	−	0.106494i
$120$	0.515640	−	0.911904i	0.0470713	−	0.0832450i
$121$	−5.09920	+	28.9190i	−0.463564	+	2.62900i
$122$	1.91022	+	2.72808i	0.172944	+	0.246989i
$123$	14.9245	−	6.63281i	1.34570	−	0.598061i
$124$	−2.24493	−	2.67541i	−0.201601	−	0.240259i
$125$	9.19665	−	6.35781i	0.822573	−	0.568659i
$126$	−13.8805	−	8.69942i	−1.23657	−	0.775006i
$127$	−0.371696	+	1.38719i	−0.0329827	+	0.123093i	−0.980454	−	0.196747i	$-0.936962\pi$
$127$	−0.371696	+	1.38719i	−0.0329827	+	0.123093i	0.947472	+	0.319840i	$0.103629\pi$
$128$	−0.912480	−	1.95682i	−0.0806526	−	0.172960i
$129$	2.96298	+	5.35383i	0.260876	+	0.471379i
$130$	−7.08862	+	6.28302i	−0.621713	+	0.551057i
$131$	−6.84812	−	18.8151i	−0.598323	−	1.64388i	−0.754614	−	0.656168i	$-0.772176\pi$
$131$	−6.84812	−	18.8151i	−0.598323	−	1.64388i	0.156291	−	0.987711i	$-0.450046\pi$
$132$	−1.62167	−	23.4167i	−0.141148	−	2.03816i
$133$	−6.87551	−	4.81428i	−0.596182	−	0.417451i
$134$	−10.8744			−0.939409
$135$	6.92149	−	9.33236i	0.595707	−	0.803202i
$136$	−0.182006			−0.0156069
$137$	−10.7088	−	7.49837i	−0.914913	−	0.640629i	0.0183463	−	0.999832i	$-0.494160\pi$
$137$	−10.7088	−	7.49837i	−0.914913	−	0.640629i	−0.933260	+	0.359202i	$0.883049\pi$
$138$	−1.43127	−	0.699266i	−0.121838	−	0.0595254i
$139$	4.79900	+	13.1851i	0.407046	+	1.11835i	0.958735	+	0.284300i	$0.0917610\pi$
$139$	4.79900	+	13.1851i	0.407046	+	1.11835i	−0.551690	+	0.834049i	$0.686017\pi$
$140$	12.7877	+	0.770420i	1.08076	+	0.0651124i
$141$	−5.60399	+	9.31245i	−0.471941	+	0.784250i
$142$	−2.03418	−	4.36232i	−0.170705	−	0.366078i
$143$	−3.42638	+	12.7874i	−0.286528	+	1.06934i
$144$	−3.43087	−	10.6076i	−0.285906	−	0.883963i
$145$	11.1675	−	14.0658i	0.927408	−	1.16810i
$146$	1.80932	+	2.15626i	0.149740	+	0.178453i
$147$	0.0390188	−	0.368858i	0.00321822	−	0.0304229i
$148$	3.49795	+	4.99559i	0.287530	+	0.410635i
$149$	0.199237	−	1.12993i	0.0163222	−	0.0925675i	−0.975558	−	0.219740i	$-0.929479\pi$
$149$	0.199237	−	1.12993i	0.0163222	−	0.0925675i	0.991881	+	0.127173i	$0.0405902\pi$
$150$	−2.43020	+	17.4377i	−0.198425	+	1.42378i
$151$	1.20809	−	1.01370i	0.0983127	−	0.0824941i	−0.592307	−	0.805713i	$-0.701783\pi$
$151$	1.20809	−	1.01370i	0.0983127	−	0.0824941i	0.690619	+	0.723219i	$0.257338\pi$
$152$	0.218772	+	0.816468i	0.0177447	+	0.0662243i
$153$	−2.00326	−	0.248699i	−0.161954	−	0.0201061i
$154$	30.0443	−	17.3461i	2.42104	−	1.39779i
$155$	3.21909	+	1.74402i	0.258564	+	0.140083i
$156$	0.139519	−	7.69709i	0.0111705	−	0.616260i
$157$	−1.15466	−	13.1978i	−0.0921516	−	1.05330i	−0.891679	−	0.452668i	$-0.850472\pi$
$157$	−1.15466	−	13.1978i	−0.0921516	−	1.05330i	0.799528	−	0.600629i	$-0.205083\pi$
$158$	12.5960	+	5.87360i	1.00208	+	0.467278i
$159$	−14.4135	−	2.81174i	−1.14306	−	0.222985i
$160$	13.1429	+	12.4494i	1.03904	+	0.984211i
$161$		−	1.21507i		−	0.0957606i
$162$	3.44300	+	17.9701i	0.270507	+	1.41186i
$163$	−13.2225	+	13.2225i	−1.03567	+	1.03567i	−0.0363256	+	0.999340i	$0.511565\pi$
$163$	−13.2225	+	13.2225i	−1.03567	+	1.03567i	−0.999340	+	0.0363256i	$0.988435\pi$
$164$	−3.49261	−	19.8076i	−0.272727	−	1.54671i
$165$	10.5987	+	22.2069i	0.825108	+	1.72880i
$166$	7.56276	−	2.75262i	0.586984	−	0.213645i
$167$	7.51125	−	0.657149i	0.581238	−	0.0508517i	0.207254	−	0.978287i	$-0.433547\pi$
$167$	7.51125	−	0.657149i	0.581238	−	0.0508517i	0.373983	+	0.927435i	$0.377992\pi$
$168$	−0.905766	+	0.873514i	−0.0698813	+	0.0673931i
$169$	2.96127	−	8.13602i	0.227790	−	0.625848i
$170$	2.84498	−	1.12367i	0.218200	−	0.0861813i
$171$	1.29228	+	9.28546i	0.0988233	+	0.710077i
$172$	7.27894	−	1.95039i	0.555014	−	0.148715i
$173$	7.48506	+	0.654858i	0.569078	+	0.0497879i	0.368064	−	0.929800i	$-0.380021\pi$
$173$	7.48506	+	0.654858i	0.569078	+	0.0497879i	0.201014	+	0.979588i	$0.435576\pi$
$174$	4.40558	+	27.9371i	0.333986	+	2.11790i
$175$	−12.7647	+	4.17326i	−0.964921	+	0.315469i
$176$	23.2516	+	4.09989i	1.75266	+	0.309041i
$177$	−13.6676	−	1.44579i	−1.02732	−	0.108672i
$178$	0.151963	−	1.73695i	0.0113901	−	0.130190i
$179$	6.45949	−	11.1882i	0.482805	−	0.836242i	−0.517000	−	0.855985i	$-0.672951\pi$
$179$	6.45949	−	11.1882i	0.482805	−	0.836242i	0.999805	+	0.0197428i	$0.00628473\pi$
$180$	−9.09685	−	11.0450i	−0.678039	−	0.823248i
$181$	−2.64164	−	4.57545i	−0.196351	−	0.340091i	0.750991	−	0.660312i	$-0.229576\pi$
$181$	−2.64164	−	4.57545i	−0.196351	−	0.340091i	−0.947343	+	0.320222i	$0.896243\pi$
$182$	10.3119	−	4.80853i	0.764371	−	0.356432i
$183$	2.75356	−	0.684578i	0.203549	−	0.0506055i
$184$	−0.0786542	+	0.0937365i	−0.00579847	+	0.00691034i
$185$	−5.33427	−	3.52369i	−0.392184	−	0.259066i
$186$	−5.45257	+	1.87338i	−0.399802	+	0.137363i
$187$	2.45207	−	3.50191i	0.179313	−	0.256085i
$188$	9.46453	+	9.46453i	0.690272	+	0.690272i
$189$	−11.1630	+	8.37674i	−0.811988	+	0.609318i
$190$	−8.46039	−	11.4118i	−0.613782	−	0.827898i
$191$	18.3259	−	3.23135i	1.32602	−	0.233812i	0.534607	−	0.845101i	$-0.320460\pi$
$191$	18.3259	−	3.23135i	1.32602	−	0.233812i	0.791408	+	0.611288i	$0.209348\pi$
$192$	−15.5972	+	1.08015i	−1.12563	+	0.0779530i
$193$	−2.42548	+	5.20146i	−0.174590	+	0.374410i	−0.974058	−	0.226300i	$-0.927337\pi$
$193$	−2.42548	+	5.20146i	−0.174590	+	0.374410i	0.799468	+	0.600709i	$0.205115\pi$
$194$	6.07563	+	5.09806i	0.436205	+	0.366020i
$195$	2.82805	+	7.55841i	0.202521	+	0.541269i
$196$	−0.429242	−	0.156231i	−0.0306601	−	0.0111594i
$197$	16.4402	+	4.40513i	1.17131	+	0.313852i	0.791475	−	0.611201i	$-0.209313\pi$
$197$	16.4402	+	4.40513i	1.17131	+	0.313852i	0.379837	+	0.925053i	$0.375980\pi$
$198$	−37.0405	−	11.3788i	−2.63236	−	0.808657i
$199$	−20.0824	−	11.5946i	−1.42361	−	0.821920i	−0.427002	−	0.904251i	$-0.640430\pi$
$199$	−20.0824	−	11.5946i	−1.42361	−	0.821920i	−0.996605	+	0.0823307i	$0.973764\pi$
$200$	1.25488	+	0.504344i	0.0887335	+	0.0356625i
$201$	−3.32598	+	8.64713i	−0.234597	+	0.609922i
$202$	−22.7045	+	15.8978i	−1.59748	+	1.11857i
$203$	−17.6716	+	12.3738i	−1.24030	+	0.868469i
$204$	−0.892456	+	2.32027i	−0.0624844	+	0.162452i
$205$	11.0330	+	17.9675i	0.770580	+	1.25490i
$206$	−11.1949	−	6.46336i	−0.779983	−	0.450324i
$207$	−0.993800	+	0.924243i	−0.0690738	+	0.0642393i
$208$	7.47961	+	2.00416i	0.518618	+	0.138963i
$209$	−18.6568	−	6.79052i	−1.29052	−	0.469710i
$210$	8.76537	−	19.2462i	0.604868	−	1.32811i
$211$	−1.99032	−	1.67007i	−0.137019	−	0.114973i	0.571702	−	0.820461i	$-0.306283\pi$
$211$	−1.99032	−	1.67007i	−0.137019	−	0.114973i	−0.708721	+	0.705488i	$0.750728\pi$
$212$	−7.64307	+	16.3906i	−0.524928	+	1.12571i
$213$	−4.09099	+	0.283312i	−0.280310	+	0.0194122i
$214$	21.0349	−	3.70902i	1.43792	−	0.253543i
$215$	−6.34591	+	4.70469i	−0.432787	+	0.320857i
$216$	1.40342	+	0.0763830i	0.0954905	+	0.00519721i
$217$	−3.10966	−	3.10966i	−0.211097	−	0.211097i
$218$	3.19212	−	4.55882i	0.216198	−	0.308762i
$219$	2.26800	−	0.779232i	0.153257	−	0.0526556i
$220$	29.6894	−	6.06858i	2.00166	−	0.409143i
$221$	0.901242	−	1.07406i	0.0606241	−	0.0722490i
$222$	9.76999	−	2.42897i	0.655719	−	0.163022i
$223$	4.57405	−	2.13291i	0.306301	−	0.142831i	−0.263390	−	0.964689i	$-0.584841\pi$
$223$	4.57405	−	2.13291i	0.306301	−	0.142831i	0.569691	+	0.821859i	$0.307063\pi$
$224$	−10.8726	−	18.8318i	−0.726453	−	1.25825i
$225$	13.1228	+	7.26581i	0.874853	+	0.484388i
$226$	−20.5868	+	35.6573i	−1.36941	+	2.37189i
$227$	−1.72288	+	19.6926i	−0.114352	+	1.30705i	0.694696	+	0.719304i	$0.255539\pi$
$227$	−1.72288	+	19.6926i	−0.114352	+	1.30705i	−0.809048	+	0.587743i	$0.800017\pi$
$228$	11.4814	+	1.21453i	0.760371	+	0.0804341i
$229$	24.6362	+	4.34402i	1.62800	+	0.287061i	0.911740	−	0.410768i	$-0.134739\pi$
$229$	24.6362	+	4.34402i	1.62800	+	0.287061i	0.716264	+	0.697829i	$0.245850\pi$
$230$	0.650756	−	1.95082i	0.0429096	−	0.128633i
$231$	−4.60410	−	29.1959i	−0.302928	−	1.92095i
$232$	2.16426	+	0.189349i	0.142091	+	0.0124313i
$233$	7.90321	−	2.11766i	0.517756	−	0.138732i	0.00952771	−	0.999955i	$-0.496967\pi$
$233$	7.90321	−	2.11766i	0.517756	−	0.138732i	0.508229	+	0.861222i	$0.330301\pi$
$234$	−11.7767	−	4.77648i	−0.769865	−	0.312248i
$235$	−12.8726	−	5.58323i	−0.839719	−	0.364210i
$236$	−5.78894	+	15.9050i	−0.376828	+	1.03533i
$237$	8.52308	−	8.21960i	0.553633	−	0.533920i
$238$	−3.66024	+	0.320230i	−0.237258	+	0.0207574i
$239$	15.0785	−	5.48812i	0.975347	−	0.354997i	0.195317	−	0.980740i	$-0.437426\pi$
$239$	15.0785	−	5.48812i	0.975347	−	0.354997i	0.780029	+	0.625743i	$0.215204\pi$
$240$	12.9892	−	6.19938i	0.838450	−	0.400169i
$241$	2.00152	+	11.3512i	0.128929	+	0.731194i	0.978896	+	0.204358i	$0.0655107\pi$
$241$	2.00152	+	11.3512i	0.128929	+	0.731194i	−0.849967	+	0.526836i	$0.823378\pi$
$242$	42.2136	−	42.2136i	2.71359	−	2.71359i
$243$	15.3425	+	2.75839i	0.984220	+	0.176951i
$244$		−	3.49429i		−	0.223699i
$245$	0.478675	−	0.0129715i	0.0305814	−	0.000828719i
$246$	−32.5885	−	6.35726i	−2.07777	−	0.405324i
$247$	−5.90147	−	2.75190i	−0.375501	−	0.175099i
$248$	0.0385992	+	0.441191i	0.00245105	+	0.0280157i
$249$	0.124267	−	6.85565i	0.00787511	−	0.434459i
$250$	−22.7291	−	0.136151i	−1.43752	−	0.00861094i
$251$	0.521180	−	0.300903i	0.0328966	−	0.0189928i	−0.483462	−	0.875366i	$-0.660621\pi$
$251$	0.521180	−	0.300903i	0.0328966	−	0.0189928i	0.516358	+	0.856373i	$0.327287\pi$
$252$	6.69448	+	15.8302i	0.421713	+	0.997212i
$253$	−0.743887	−	2.77622i	−0.0467677	−	0.174540i
$254$	2.23656	−	1.87670i	0.140334	−	0.117755i
$255$	−0.0233704	−	2.60595i	−0.00146351	−	0.163191i
$256$	2.37270	−	13.4562i	0.148294	−	0.841014i
$257$	−5.05815	−	7.22379i	−0.315519	−	0.450608i	0.629799	−	0.776758i	$-0.283137\pi$
$257$	−5.05815	−	7.22379i	−0.315519	−	0.450608i	−0.945318	+	0.326151i	$0.894248\pi$
$258$	1.30863	−	12.3709i	0.0814718	−	0.770181i
$259$	4.93607	+	5.88259i	0.306713	+	0.365526i
$260$	9.87361	−	1.13408i	0.612336	−	0.0703327i
$261$	23.5624	+	5.04141i	1.45848	+	0.312055i
$262$	−10.5354	+	39.3187i	−0.650880	+	2.42912i
$263$	5.05420	+	10.8388i	0.311656	+	0.668347i	0.998278	−	0.0586671i	$-0.0186850\pi$
$263$	5.05420	+	10.8388i	0.311656	+	0.668347i	−0.686622	+	0.727015i	$0.740907\pi$
$264$	−1.53474	+	2.55036i	−0.0944568	+	0.156964i
$265$	1.14013	−	18.9242i	0.0700374	−	1.16250i
$266$	5.83616	+	16.0347i	0.357838	+	0.983152i
$267$	−1.33471	−	0.652089i	−0.0816827	−	0.0399072i
$268$	9.34624	+	6.54431i	0.570913	+	0.399757i
$269$	−15.6712			−0.955492			−0.477746	−	0.878498i	$-0.658546\pi$
$269$	−15.6712			−0.955492			−0.477746	+	0.878498i	$0.658546\pi$
$270$	−22.4088	+	7.47046i	−1.36376	+	0.454638i
$271$	15.3544			0.932711			0.466355	−	0.884597i	$-0.345567\pi$
$271$	15.3544			0.932711			0.466355	+	0.884597i	$0.345567\pi$
$272$	−2.04834	−	1.43426i	−0.124199	−	0.0869648i
$273$	−0.669710	−	9.67054i	−0.0405327	−	0.585287i
$274$	9.08998	+	24.9745i	0.549146	+	1.50876i
$275$	−26.6103	+	17.3500i	−1.60466	+	1.04624i
$276$	0.809308	+	1.46234i	0.0487146	+	0.0880227i
$277$	1.83097	+	3.92654i	0.110013	+	0.235923i	0.953605	−	0.301062i	$-0.0973411\pi$
$277$	1.83097	+	3.92654i	0.110013	+	0.235923i	−0.843592	+	0.536985i	$0.819563\pi$
$278$	7.38296	−	27.5536i	0.442800	−	1.65255i
$279$	−0.178013	+	4.90875i	−0.0106574	+	0.293879i
$280$	−1.27228	−	1.01013i	−0.0760335	−	0.0603666i
$281$	−11.4406	−	13.6344i	−0.682490	−	0.813360i	0.307935	−	0.951407i	$-0.400362\pi$
$281$	−11.4406	−	13.6344i	−0.682490	−	0.813360i	−0.990426	+	0.138047i	$0.955918\pi$
$282$	20.1915	−	8.97361i	1.20239	−	0.534371i
$283$	−11.3847	−	16.2591i	−0.676752	−	0.966501i	−0.999798	−	0.0201182i	$-0.993596\pi$
$283$	−11.3847	−	16.2591i	−0.676752	−	0.966501i	0.323046	−	0.946383i	$-0.395293\pi$
$284$	−0.876956	+	4.97347i	−0.0520378	+	0.295121i
$285$	−11.6621	+	3.23720i	−0.690800	+	0.191755i
$286$	20.6172	−	17.2998i	1.21912	−	1.02296i
$287$	−6.55492	−	24.4633i	−0.386925	−	1.44402i
$288$	−7.13226	+	23.2171i	−0.420273	+	1.36808i
$289$	14.3303	−	8.27362i	0.842960	−	0.486683i
$290$	−34.9992	+	10.4020i	−2.05523	+	0.610825i
$291$	5.91213	−	3.27196i	0.346575	−	0.191806i
$292$	−0.257400	−	2.94209i	−0.0150632	−	0.172173i
$293$	−14.9126	−	6.95384i	−0.871201	−	0.406248i	−0.0649974	−	0.997885i	$-0.520704\pi$
$293$	−14.9126	−	6.95384i	−0.871201	−	0.406248i	−0.806204	+	0.591638i	$0.798482\pi$
$294$	−0.495096	+	0.568771i	−0.0288746	+	0.0331714i
$295$	−0.480642	−	17.7367i	−0.0279840	−	1.03267i
$296$		−	0.773337i		−	0.0449493i
$297$	−20.3772	+	25.9736i	−1.18240	+	1.50714i
$298$	−1.64938	+	1.64938i	−0.0955460	+	0.0955460i
$299$	−0.163687	−	0.928314i	−0.00946626	−	0.0536858i
$300$	12.5828	−	13.5246i	0.726468	−	0.780845i
$301$	8.91665	−	3.24540i	0.513947	−	0.187061i
$302$	−3.19392	+	0.279431i	−0.183789	+	0.0160795i
$303$	5.69740	+	22.9165i	0.327307	+	1.31652i
$304$	−3.97190	+	10.9127i	−0.227804	+	0.625887i
$305$	1.34562	+	3.40694i	0.0770500	+	0.195081i
$306$	3.04609	+	2.75012i	0.174133	+	0.157214i
$307$	−2.83491	+	0.759611i	−0.161797	+	0.0433533i	−0.338808	−	0.940856i	$-0.610024\pi$
$307$	−2.83491	+	0.759611i	−0.161797	+	0.0433533i	0.177011	+	0.984209i	$0.443357\pi$
$308$	−36.2611	−	3.17243i	−2.06617	−	0.180766i
$309$	−8.56351	+	6.92509i	−0.487161	+	0.393955i
$310$	−3.32718	−	6.65808i	−0.188971	−	0.378153i
$311$	−3.75166	−	0.661519i	−0.212737	−	0.0375113i	0.0662637	−	0.997802i	$-0.478892\pi$
$311$	−3.75166	−	0.661519i	−0.212737	−	0.0375113i	−0.279001	+	0.960291i	$0.590003\pi$
$312$	−0.574333	+	0.789387i	−0.0325152	+	0.0446902i
$313$	0.0495580	−	0.566450i	0.00280118	−	0.0320177i	−0.994665	−	0.103153i	$-0.967107\pi$
$313$	0.0495580	−	0.566450i	0.00280118	−	0.0320177i	0.997467	+	0.0711357i	$0.0226623\pi$
$314$	−13.4667	+	23.3250i	−0.759971	+	1.31631i
$315$	−12.6232	−	12.8565i	−0.711239	−	0.724384i
$316$	−7.29107	−	12.6285i	−0.410155	−	0.710409i
$317$	−10.3800	+	4.84025i	−0.582997	+	0.271856i	−0.691661	−	0.722223i	$-0.743121\pi$
$317$	−10.3800	+	4.84025i	−0.582997	+	0.271856i	0.108664	+	0.994079i	$0.465343\pi$
$318$	20.7245	+	21.4897i	1.16217	+	1.20508i
$319$	−32.8012	+	39.0909i	−1.83651	+	2.18867i
$320$	−4.04212	−	19.7753i	−0.225961	−	1.10547i
$321$	3.48425	−	17.8609i	0.194472	−	0.996900i
$322$	−1.41686	+	2.02348i	−0.0789584	+	0.112764i
$323$	1.48686	+	1.48686i	0.0827312	+	0.0827312i
$324$	7.85534	−	17.5167i	0.436408	−	0.973151i
$325$	−9.19007	+	4.90798i	−0.509774	+	0.272246i
$326$	37.4382	−	6.60137i	2.07351	−	0.365616i
$327$	−2.64876	−	3.93263i	−0.146477	−	0.217475i
$328$	−1.07789	+	2.31154i	−0.0595165	+	0.127634i
$329$	12.9110	+	10.8336i	0.711806	+	0.597276i
$330$	8.24455	−	49.3406i	0.453847	−	2.71611i
$331$	24.0043	+	8.73685i	1.31940	+	0.480221i	0.903265	−	0.429084i	$-0.141164\pi$
$331$	24.0043	+	8.73685i	1.31940	+	0.480221i	0.416131	+	0.909305i	$0.363386\pi$
$332$	−8.15650	−	2.18553i	−0.447646	−	0.119946i
$333$	1.05671	−	8.51181i	0.0579076	−	0.466444i
$334$	−13.2750	−	7.66431i	−0.726374	−	0.419372i
$335$	−11.6328	−	2.78156i	−0.635566	−	0.151973i
$336$	−17.0773	+	2.69303i	−0.931641	+	0.146917i
$337$	14.4868	−	10.1438i	0.789147	−	0.552566i	−0.108077	−	0.994143i	$-0.534469\pi$
$337$	14.4868	−	10.1438i	0.789147	−	0.552566i	0.897224	+	0.441576i	$0.145580\pi$
$338$	−14.4187	+	10.0961i	−0.784274	+	0.549154i
$339$	22.0574	+	27.2761i	1.19800	+	1.48143i
$340$	−3.12140	−	0.746372i	−0.169282	−	0.0404777i
$341$	−9.00884	−	5.20126i	−0.487856	−	0.281664i
$342$	8.67547	−	16.9702i	0.469116	−	0.917645i
$343$	17.6052	+	4.71730i	0.950591	+	0.254710i
$344$	−0.897959	−	0.326830i	−0.0484147	−	0.0176215i
$345$	−1.35221	−	1.11413i	−0.0728007	−	0.0599828i
$346$	−11.7015	−	9.81869i	−0.629075	−	0.527856i
$347$	0.943762	−	2.02390i	0.0506638	−	0.108649i	−0.879346	−	0.476183i	$-0.842020\pi$
$347$	0.943762	−	2.02390i	0.0506638	−	0.108649i	0.930010	+	0.367534i	$0.119798\pi$
$348$	13.0262	−	26.6623i	0.698280	−	1.42925i
$349$	−18.9031	+	3.33312i	−1.01186	+	0.178418i	−0.654910	−	0.755707i	$-0.727294\pi$
$349$	−18.9031	+	3.33312i	−1.01186	+	0.178418i	−0.356948	+	0.934124i	$0.616183\pi$
$350$	26.1238	+	7.93475i	1.39637	+	0.424130i
$351$	−7.40009	+	7.90367i	−0.394988	+	0.421867i
$352$	−36.3712	−	36.3712i	−1.93859	−	1.93859i
$353$	17.0436	−	24.3407i	0.907137	−	1.29553i	−0.0478427	−	0.998855i	$-0.515235\pi$
$353$	17.0436	−	24.3407i	0.907137	−	1.29553i	0.954980	−	0.296671i	$-0.0958765\pi$
$354$	21.0751	+	18.3451i	1.12013	+	0.975032i
$355$	−1.06020	−	5.18685i	−0.0562698	−	0.275289i
$356$	−1.17591	+	1.40140i	−0.0623233	+	0.0742741i
$357$	−0.864856	+	3.00849i	−0.0457730	+	0.159226i
$358$	−23.8034	+	11.0997i	−1.25805	+	0.586638i
$359$	14.0984	+	24.4191i	0.744085	+	1.28879i	0.950621	+	0.310354i	$0.100448\pi$
$359$	14.0984	+	24.4191i	0.744085	+	1.28879i	−0.206536	+	0.978439i	$0.566219\pi$
$360$	0.141586	+	1.80895i	0.00746221	+	0.0953402i
$361$	−4.61724	+	7.99729i	−0.243012	+	0.420910i
$362$	−0.936127	+	10.7000i	−0.0492017	+	0.562378i
$363$	−20.6562	−	46.4785i	−1.08417	−	2.43949i
$364$	−11.7566	−	2.07300i	−0.616212	−	0.108655i
$365$	1.38394	+	2.76943i	0.0724388	+	0.144958i
$366$	−5.38386	−	2.07081i	−0.281419	−	0.108243i
$367$	23.9655	+	2.09671i	1.25099	+	0.109447i	0.693328	−	0.720622i	$-0.256144\pi$
$367$	23.9655	+	2.09671i	1.25099	+	0.109447i	0.557660	+	0.830069i	$0.311699\pi$
$368$	−1.62387	+	0.435114i	−0.0846499	+	0.0226819i
$369$	−15.0225	+	23.9693i	−0.782038	+	1.24779i
$370$	4.77443	+	12.0883i	0.248211	+	0.628438i
$371$	−7.78866	+	21.3992i	−0.404367	+	1.11099i
$372$	5.81373	+	1.67128i	0.301428	+	0.0866519i
$373$	7.15282	−	0.625791i	0.370359	−	0.0324022i	0.0995428	−	0.995033i	$-0.468262\pi$
$373$	7.15282	−	0.625791i	0.370359	−	0.0324022i	0.270816	+	0.962631i	$0.412706\pi$
$374$	−8.16699	+	2.97254i	−0.422305	+	0.153706i
$375$	−7.06003	+	18.0321i	−0.364579	+	0.931173i
$376$	−0.294734	−	1.67152i	−0.0151998	−	0.0862021i
$377$	−11.8342	+	11.8342i	−0.609494	+	0.609494i
$378$	28.3579	−	0.933134i	1.45858	−	0.0479952i
$379$		−	6.61098i		−	0.339583i	−0.985480	−	0.169792i	$-0.945691\pi$
$379$		−	6.61098i		−	0.339583i	0.985480	−	0.169792i	$-0.0543094\pi$
$380$	0.403760	+	14.8996i	0.0207125	+	0.764333i
$381$	−0.808252	−	2.35246i	−0.0414080	−	0.120520i
$382$	−34.2866	−	15.9881i	−1.75426	−	0.818023i
$383$	0.852747	+	9.74694i	0.0435733	+	0.498046i	0.986355	+	0.164634i	$0.0526443\pi$
$383$	0.852747	+	9.74694i	0.0435733	+	0.498046i	−0.942781	+	0.333412i	$0.891800\pi$
$384$	3.20425	+	1.92823i	0.163516	+	0.0983998i
$385$	36.5763	−	10.8707i	1.86410	−	0.554022i
$386$	10.1045	−	5.83385i	0.514307	−	0.296935i
$387$	−9.43687	−	4.82429i	−0.479703	−	0.245232i
$388$	−2.15377	−	8.03798i	−0.109341	−	0.408067i
$389$	7.47118	−	6.26906i	0.378804	−	0.317854i	−0.433429	−	0.901188i	$-0.642696\pi$
$389$	7.47118	−	6.26906i	0.378804	−	0.317854i	0.812233	+	0.583334i	$0.198252\pi$
$390$	4.10404	−	15.8850i	0.207816	−	0.804366i
$391$	−0.0528585	+	0.299776i	−0.00267317	+	0.0151603i
$392$	0.0332242	+	0.0474490i	0.00167807	+	0.00239654i
$393$	28.0431	+	20.4033i	1.41459	+	1.02921i
$394$	−22.2415	−	26.5064i	−1.12051	−	1.33538i
$395$	11.9719	+	9.50510i	0.602374	+	0.478253i
$396$	24.9874	+	32.0710i	1.25566	+	1.61163i
$397$	−5.87091	+	21.9105i	−0.294653	+	1.09966i	0.646840	+	0.762626i	$0.276090\pi$
$397$	−5.87091	+	21.9105i	−0.294653	+	1.09966i	−0.941493	+	0.337033i	$0.890577\pi$
$398$	19.9237	+	42.7265i	0.998684	+	2.14168i
$399$	14.5355	+	0.263474i	0.727685	+	0.0131902i
$400$	10.1484	+	15.5648i	0.507418	+	0.778242i
$401$	10.7416	+	29.5124i	0.536411	+	1.47378i	0.851316	+	0.524654i	$0.175805\pi$
$401$	10.7416	+	29.5124i	0.536411	+	1.47378i	−0.314905	+	0.949123i	$0.601973\pi$
$402$	15.6221	−	10.5220i	0.779157	−	0.524788i
$403$	−2.79470	−	1.95687i	−0.139214	−	0.0974788i
$404$	29.0812			1.44684
$405$	−0.913442	+	20.1039i	−0.0453893	+	0.998969i
$406$	43.8578			2.17662
$407$	14.8795	+	10.4188i	0.737551	+	0.516439i
$408$	0.261467	−	0.176106i	0.0129445	−	0.00871856i
$409$	−9.77070	−	26.8448i	−0.483130	−	1.32739i	−0.906796	−	0.421570i	$-0.861479\pi$
$409$	−9.77070	−	26.8448i	−0.483130	−	1.32739i	0.423666	−	0.905818i	$-0.360743\pi$
$410$	2.57779	−	42.7871i	0.127308	−	2.11310i
$411$	22.6394	+	0.410367i	1.11672	+	0.0202419i
$412$	5.73195	+	12.2922i	0.282393	+	0.605593i
$413$	−5.51614	+	20.5865i	−0.271432	+	1.01300i
$414$	2.73274	−	0.380323i	0.134307	−	0.0186918i
$415$	8.79424	−	1.01010i	0.431692	−	0.0495840i
$416$	−10.8436	−	12.9229i	−0.531650	−	0.633596i
$417$	−19.6519	−	14.2981i	−0.962360	−	0.700182i
$418$	23.1514	+	33.0637i	1.13237	+	1.61720i
$419$	0.704690	−	3.99650i	0.0344264	−	0.195242i	−0.962744	−	0.270414i	$-0.912839\pi$
$419$	0.704690	−	3.99650i	0.0344264	−	0.195242i	0.997171	+	0.0751721i	$0.0239506\pi$
$420$	−19.1160	+	11.2664i	−0.932767	+	0.549745i
$421$	−7.52582	+	6.31491i	−0.366786	+	0.307770i	−0.807489	−	0.589883i	$-0.799174\pi$
$421$	−7.52582	+	6.31491i	−0.366786	+	0.307770i	0.440703	+	0.897653i	$0.354729\pi$
$422$	1.36710	+	5.10208i	0.0665493	+	0.248366i
$423$	−0.959995	−	18.8005i	−0.0466765	−	0.914110i
$424$	1.98608	−	1.14666i	0.0964525	−	0.0556869i
$425$	3.33080	−	0.474311i	0.161567	−	0.0230075i
$426$	7.14320	+	4.29860i	0.346089	+	0.208268i
$427$	−0.383483	−	4.38323i	−0.0185581	−	0.212119i
$428$	−20.3110	−	9.47115i	−0.981767	−	0.457805i
$429$	−7.45066	−	21.6855i	−0.359721	−	1.04699i
$430$	16.0540	−	0.435044i	0.774194	−	0.0209797i
$431$		−	3.57709i		−	0.172302i	−0.996282	−	0.0861512i	$-0.972543\pi$
$431$		−	3.57709i		−	0.172302i	0.996282	−	0.0861512i	$-0.0274568\pi$
$432$	15.1925	+	11.9190i	0.730949	+	0.573453i
$433$	0.671243	−	0.671243i	0.0322579	−	0.0322579i	−0.690794	−	0.723052i	$-0.742739\pi$
$433$	0.671243	−	0.671243i	0.0322579	−	0.0322579i	0.723052	+	0.690794i	$0.242739\pi$
$434$	1.55251	+	8.80470i	0.0745227	+	0.422639i
$435$	−2.43318	+	31.0121i	−0.116662	+	1.48692i
$436$	−5.48705	+	1.99712i	−0.262782	+	0.0956449i
$437$	1.40831	−	0.123211i	0.0673688	−	0.00589400i
$438$	−4.68560	−	1.34698i	−0.223887	−	0.0643611i
$439$	11.2524	−	30.9157i	0.537048	−	1.47553i	−0.313479	−	0.949595i	$-0.601495\pi$
$439$	11.2524	−	30.9157i	0.537048	−	1.47553i	0.850527	−	0.525932i	$-0.176283\pi$
$440$	−3.52537	−	1.52905i	−0.168066	−	0.0728948i
$441$	0.300849	+	0.567650i	0.0143261	+	0.0270310i
$442$	−2.75330	+	0.737744i	−0.130961	+	0.0350909i
$443$	−22.3331	−	1.95389i	−1.06108	−	0.0928322i	−0.456771	−	0.889585i	$-0.650994\pi$
$443$	−22.3331	−	1.95389i	−1.06108	−	0.0928322i	−0.604306	+	0.796752i	$0.706550\pi$
$444$	−9.85878	−	3.79202i	−0.467877	−	0.179961i
$445$	0.606852	−	1.81920i	0.0287676	−	0.0862385i
$446$	−10.1044	−	1.78168i	−0.478459	−	0.0843652i
$447$	0.807085	+	1.81602i	0.0381738	+	0.0858948i
$448$	−2.11307	+	24.1525i	−0.0998333	+	1.14110i
$449$	4.96273	−	8.59571i	0.234206	−	0.405656i	−0.724836	−	0.688922i	$-0.758084\pi$
$449$	4.96273	−	8.59571i	0.234206	−	0.405656i	0.959042	+	0.283265i	$0.0914177\pi$
$450$	−13.3813	−	27.4021i	−0.630800	−	1.29175i
$451$	−29.9538	−	51.8815i	−1.41047	−	2.44301i
$452$	39.1525	−	18.2571i	1.84158	−	0.858742i
$453$	−0.754671	+	2.62520i	−0.0354575	+	0.123343i
$454$	25.8323	−	30.7857i	1.21237	−	1.44484i
$455$	12.2610	−	2.50618i	0.574804	−	0.117491i
$456$	−1.10429	−	0.961244i	−0.0517130	−	0.0450144i
$457$	19.8172	−	28.3019i	0.927010	−	1.32391i	−0.0190173	−	0.999819i	$-0.506054\pi$
$457$	19.8172	−	28.3019i	0.927010	−	1.32391i	0.946027	−	0.324088i	$-0.105057\pi$
$458$	−35.9619	−	35.9619i	−1.68039	−	1.68039i
$459$	3.11849	−	1.58105i	0.145559	−	0.0737972i
$460$	−1.73332	+	1.28504i	−0.0808164	+	0.0599152i
$461$	−10.2855	+	1.81362i	−0.479046	+	0.0844687i	−0.407957	−	0.913001i	$-0.633759\pi$
$461$	−10.2855	+	1.81362i	−0.479046	+	0.0844687i	−0.0710890	+	0.997470i	$0.522647\pi$
$462$	−26.3773	+	53.9895i	−1.22718	+	2.51182i
$463$	−7.80727	+	16.7427i	−0.362835	+	0.778101i	0.637138	+	0.770749i	$0.280118\pi$
$463$	−7.80727	+	16.7427i	−0.362835	+	0.778101i	−0.999973	+	0.00735185i	$0.997660\pi$
$464$	22.8650	+	19.1860i	1.06148	+	0.890689i
$465$	−6.31199	+	0.609313i	−0.292712	+	0.0282562i
$466$	−15.6308	−	5.68914i	−0.724082	−	0.263544i
$467$	−37.1950	−	9.96636i	−1.72118	−	0.461188i	−0.743057	−	0.669228i	$-0.766625\pi$
$467$	−37.1950	−	9.96636i	−1.72118	−	0.461188i	−0.978120	+	0.208040i	$0.933292\pi$
$468$	7.24717	+	11.1925i	0.335001	+	0.517374i
$469$	12.4421	+	7.18347i	0.574524	+	0.331702i
$470$	14.9267	+	24.3084i	0.688518	+	1.12126i
$471$	14.4288	+	17.8425i	0.664842	+	0.822139i
$472$	1.75816	−	1.23108i	0.0809259	−	0.0566649i
$473$	18.3862	−	12.8741i	0.845397	−	0.591953i
$474$	−23.7784	+	3.74977i	−1.09218	+	0.172233i
$475$	−6.13137	−	14.3717i	−0.281327	−	0.659417i
$476$	3.33858	+	1.92753i	0.153024	+	0.0883482i
$477$	23.4268	−	9.90701i	1.07264	−	0.453611i
$478$	−31.5102	−	8.44313i	−1.44124	−	0.386180i
$479$	13.8251	+	5.03191i	0.631684	+	0.229914i	0.637964	−	0.770066i	$-0.279777\pi$
$479$	13.8251	+	5.03191i	0.631684	+	0.229914i	−0.00628038	+	0.999980i	$0.501999\pi$
$480$	−30.9268	−	5.16770i	−1.41161	−	0.235872i
$481$	4.56365	+	3.82935i	0.208084	+	0.174604i
$482$	9.90315	−	21.2374i	0.451076	−	0.967336i
$483$	1.17568	+	1.74555i	0.0534954	+	0.0794251i
$484$	−61.6857	+	10.8768i	−2.80389	+	0.494402i
$485$	5.19529	+	7.00765i	0.235906	+	0.318201i
$486$	−22.3337	−	22.4841i	−1.01308	−	1.01990i
$487$	3.40980	+	3.40980i	0.154513	+	0.154513i	0.780130	−	0.625617i	$-0.215153\pi$
$487$	3.40980	+	3.40980i	0.154513	+	0.154513i	−0.625617	+	0.780130i	$0.715153\pi$
$488$	−0.254154	+	0.362969i	−0.0115050	+	0.0164308i
$489$	6.20132	−	31.7891i	0.280433	−	1.43755i
$490$	−0.812277	−	0.536569i	−0.0366949	−	0.0242397i
$491$	−4.15599	+	4.95292i	−0.187557	+	0.223522i	−0.851627	−	0.524149i	$-0.824383\pi$
$491$	−4.15599	+	4.95292i	−0.187557	+	0.223522i	0.664069	+	0.747671i	$0.268828\pi$
$492$	24.1830	+	25.0759i	1.09025	+	1.13051i
$493$	4.89815	−	2.28404i	0.220602	−	0.102868i
$494$	6.61896	+	11.4644i	0.297801	+	0.515806i
$495$	−36.7130	−	21.6469i	−1.65013	−	0.972954i
$496$	−3.04231	+	5.26944i	−0.136604	+	0.236605i
$497$	−0.554237	+	6.33496i	−0.0248609	+	0.284162i
$498$	−8.20115	+	11.2720i	−0.367502	+	0.505110i
$499$	−24.8022	−	4.37330i	−1.11030	−	0.195776i	−0.411722	−	0.911309i	$-0.635073\pi$
$499$	−24.8022	−	4.37330i	−1.11030	−	0.195776i	−0.698578	+	0.715534i	$0.746184\pi$
$500$	19.4530	+	13.7955i	0.869966	+	0.616956i
$501$	−10.1547	+	8.21183i	−0.453678	+	0.366878i
$502$	−1.21881	−	0.106632i	−0.0543982	−	0.00475922i
$503$	−37.5360	+	10.0577i	−1.67365	+	0.448452i	−0.966090	−	0.258205i	$-0.916869\pi$
$503$	−37.5360	+	10.0577i	−1.67365	+	0.448452i	−0.707556	+	0.706657i	$0.750202\pi$
$504$	0.456008	−	2.13128i	0.0203122	−	0.0949349i
$505$	−28.3542	+	11.1989i	−1.26175	+	0.498345i
$506$	−1.99847	+	5.49075i	−0.0888428	+	0.244094i
$507$	3.61819	+	14.5534i	0.160690	+	0.646338i
$508$	−3.05166	+	0.266986i	−0.135396	+	0.0118456i
$509$	5.50573	−	2.00392i	0.244037	−	0.0888223i	−0.217106	−	0.976148i	$-0.569662\pi$
$509$	5.50573	−	2.00392i	0.244037	−	0.0888223i	0.461143	+	0.887326i	$0.347439\pi$
$510$	−2.99981	+	4.36701i	−0.132834	+	0.193374i
$511$	−0.645765	−	3.66231i	−0.0285669	−	0.162011i
$512$	−22.6957	+	22.6957i	−1.00302	+	1.00302i
$513$	−10.8410	−	12.0890i	−0.478640	−	0.533740i
$514$			17.9282i			0.790777i
$515$	−10.3223	−	9.77760i	−0.454854	−	0.430853i
$516$	−8.56964	+	9.84490i	−0.377258	+	0.433397i
$517$	36.1320	+	16.8486i	1.58908	+	0.741002i
$518$	−1.36065	−	15.5523i	−0.0597834	−	0.683327i
$519$	−11.3866	+	6.30168i	−0.499814	+	0.276613i
$520$	−1.10811	−	0.600345i	−0.0485937	−	0.0263269i
$521$	16.6908	−	9.63645i	0.731238	−	0.422180i	−0.0876370	−	0.996152i	$-0.527932\pi$
$521$	16.6908	−	9.63645i	0.731238	−	0.422180i	0.818875	+	0.573972i	$0.194598\pi$
$522$	−33.3605	−	35.8712i	−1.46015	−	1.57004i
$523$	5.63988	+	21.0483i	0.246615	+	0.920379i	0.972565	+	0.232631i	$0.0747336\pi$
$523$	5.63988	+	21.0483i	0.246615	+	0.920379i	−0.725950	+	0.687747i	$0.758600\pi$
$524$	32.7171	−	27.4529i	1.42925	−	1.19929i
$525$	14.2996	−	18.3462i	0.624085	−	0.800694i
$526$	4.22192	−	23.9437i	0.184084	−	1.04399i
$527$	0.631923	+	0.902479i	0.0275270	+	0.0393126i
$528$	−37.3700	+	16.6081i	−1.62632	+	0.722777i
$529$	−14.6526	−	17.4623i	−0.637068	−	0.759228i
$530$	−23.9657	+	30.1855i	−1.04100	+	1.31117i
$531$	21.0335	−	11.1475i	0.912777	−	0.483762i
$532$	4.63380	−	17.2936i	0.200901	−	0.749772i
$533$	−8.30354	−	17.8070i	−0.359666	−	0.771307i
$534$	1.46234	+	2.64231i	0.0632816	+	0.114344i
$535$	23.4505	+	1.41282i	1.01385	+	0.0610817i
$536$	−0.494847	−	1.35958i	−0.0213741	−	0.0587249i
$537$	1.54592	+	22.3229i	0.0667112	+	0.963302i
$538$	26.0978	+	18.2738i	1.12515	+	0.787841i
$539$	−1.36056			−0.0586036
$540$	23.7554	+	7.06513i	1.02227	+	0.304035i
$541$	17.4882			0.751877			0.375938	−	0.926645i	$-0.377320\pi$
$541$	17.4882			0.751877			0.375938	+	0.926645i	$0.377320\pi$
$542$	−25.5700	−	17.9043i	−1.09833	−	0.769057i
$543$	8.22208	+	4.01701i	0.352843	+	0.172386i
$544$	1.86319	+	5.11909i	0.0798838	+	0.219479i
$545$	4.58081	−	4.06022i	0.196221	−	0.173921i
$546$	−10.1613	+	16.8855i	−0.434863	+	0.722635i
$547$	−15.2727	−	32.7524i	−0.653013	−	1.40039i	−0.901937	−	0.431868i	$-0.857855\pi$
$547$	−15.2727	−	32.7524i	−0.653013	−	1.40039i	0.248924	−	0.968523i	$-0.419923\pi$
$548$	7.21727	−	26.9352i	0.308306	−	1.15062i
$549$	−3.29334	+	3.64777i	−0.140556	+	0.155683i
$550$	64.5462	+	2.13611i	2.75226	+	0.0910841i
$551$	−16.1337	−	19.2274i	−0.687319	−	0.819115i
$552$	0.0222953	−	0.210765i	0.000948951	−	0.00897076i
$553$	−10.5318	−	15.0410i	−0.447859	−	0.639610i
$554$	1.52946	−	8.67402i	0.0649807	−	0.368524i
$555$	11.0726	−	0.0993003i	0.470006	−	0.00421506i
$556$	−22.9273	+	19.2383i	−0.972336	+	0.815887i
$557$	−0.942784	−	3.51852i	−0.0399470	−	0.149084i	0.943072	−	0.332589i	$-0.107922\pi$
$557$	−0.942784	−	3.51852i	−0.0399470	−	0.149084i	−0.983019	+	0.183505i	$0.941256\pi$
$558$	6.02042	−	7.96710i	0.254865	−	0.337274i
$559$	6.37515	−	3.68069i	0.269640	−	0.155677i
$560$	−6.35848	−	21.3942i	−0.268695	−	0.904070i
$561$	−0.134195	+	7.40338i	−0.00566574	+	0.312571i
$562$	3.15365	+	36.0464i	0.133029	+	1.52053i
$563$	7.85254	+	3.66170i	0.330945	+	0.154322i	0.580987	−	0.813913i	$-0.302667\pi$
$563$	7.85254	+	3.66170i	0.330945	+	0.154322i	−0.250042	+	0.968235i	$0.580444\pi$
$564$	−22.7543	−	4.43884i	−0.958131	−	0.186909i
$565$	−31.1431	+	32.8780i	−1.31020	+	1.38319i
$566$			40.3521i			1.69613i
$567$	7.93136	−	22.8351i	0.333086	−	0.958982i
$568$	0.452834	−	0.452834i	0.0190005	−	0.0190005i
$569$	−6.84317	−	38.8095i	−0.286881	−	1.62698i	−0.698490	−	0.715620i	$-0.746144\pi$
$569$	−6.84317	−	38.8095i	−0.286881	−	1.62698i	0.411609	−	0.911361i	$-0.364967\pi$
$570$	23.1960	+	8.20783i	0.971572	+	0.343788i
$571$	−4.05495	+	1.47588i	−0.169694	+	0.0617636i	−0.425470	−	0.904972i	$-0.639891\pi$
$571$	−4.05495	+	1.47588i	−0.169694	+	0.0617636i	0.255776	+	0.966736i	$0.417669\pi$
$572$	−28.1310	+	2.46114i	−1.17621	+	0.102905i
$573$	−23.2001	+	22.3740i	−0.969198	+	0.934687i
$574$	−17.6100	+	48.3830i	−0.735026	+	2.01947i
$575$	1.19513	−	1.92040i	0.0498405	−	0.0800863i
$576$	21.3616	−	16.6434i	0.890067	−	0.693475i
$577$	29.3682	−	7.86919i	1.22261	−	0.327598i	0.410915	−	0.911674i	$-0.365209\pi$
$577$	29.3682	−	7.86919i	1.22261	−	0.327598i	0.811699	+	0.584075i	$0.198543\pi$
$578$	−33.5123	−	2.93195i	−1.39393	−	0.121953i
$579$	−1.54846	−	9.81921i	−0.0643517	−	0.408072i
$580$	36.3407	+	12.1226i	1.50897	+	0.503363i
$581$	−10.4714	−	1.84638i	−0.434425	−	0.0766009i
$582$	−13.6610	−	1.44509i	−0.566266	−	0.0599011i
$583$	−4.69481	+	53.6619i	−0.194439	+	2.22245i
$584$	−0.187253	+	0.324332i	−0.00774858	+	0.0134209i
$585$	−11.3762	−	8.12191i	−0.470346	−	0.335800i
$586$	16.7256	+	28.9696i	0.690929	+	1.19672i
$587$	17.8591	−	8.32785i	0.737126	−	0.343727i	−0.0175318	−	0.999846i	$-0.505581\pi$
$587$	17.8591	−	8.32785i	0.737126	−	0.343727i	0.754657	+	0.656119i	$0.227803\pi$
$588$	0.767809	−	0.190889i	0.0316639	−	0.00787214i
$589$	3.28890	−	3.91956i	0.135517	−	0.161503i
$590$	−19.8819	+	30.0978i	−0.818524	+	1.23911i
$591$	−27.8800	+	9.57894i	−1.14683	+	0.394025i
$592$	6.09413	−	8.70333i	0.250467	−	0.357705i
$593$	−1.60584	−	1.60584i	−0.0659438	−	0.0659438i	0.673366	−	0.739310i	$-0.264848\pi$
$593$	−1.60584	−	1.60584i	−0.0659438	−	0.0659438i	−0.739310	+	0.673366i	$0.764848\pi$
$594$	64.2219	−	19.4933i	2.63506	−	0.799821i
$595$	−3.99740	−	0.593688i	−0.163877	−	0.0243388i
$596$	2.41020	−	0.424983i	0.0987255	−	0.0174080i
$597$	40.0689	−	2.77488i	1.63991	−	0.113568i
$598$	−0.809892	+	1.73682i	−0.0331190	+	0.0710238i
$599$	−16.1072	−	13.5155i	−0.658122	−	0.552230i	0.251401	−	0.967883i	$-0.419109\pi$
$599$	−16.1072	−	13.5155i	−0.658122	−	0.552230i	−0.909523	+	0.415653i	$0.863553\pi$
$600$	−2.29074	+	0.489674i	−0.0935190	+	0.0199908i
$601$	−25.6301	−	9.32859i	−1.04547	−	0.380521i	−0.238521	−	0.971137i	$-0.576662\pi$
$601$	−25.6301	−	9.32859i	−1.04547	−	0.380521i	−0.806952	+	0.590616i	$0.798885\pi$
$602$	−18.6335	−	4.99284i	−0.759446	−	0.203493i
$603$	−3.58880	−	15.6405i	−0.146147	−	0.636931i
$604$	2.91323	+	1.68196i	0.118538	+	0.0684378i
$605$	55.9551	−	34.3596i	2.27490	−	1.39692i
$606$	17.2343	−	44.8071i	0.700097	−	1.82016i
$607$	−27.5055	+	19.2596i	−1.11641	+	0.781721i	−0.977990	−	0.208652i	$-0.933092\pi$
$607$	−27.5055	+	19.2596i	−1.11641	+	0.781721i	−0.138424	+	0.990373i	$0.544204\pi$
$608$	20.7244	−	14.5114i	0.840484	−	0.588513i
$609$	13.4140	−	34.8748i	0.543564	−	1.41320i
$610$	1.73185	−	7.24277i	0.0701205	−	0.293251i
$611$	11.3235	+	6.53761i	0.458099	+	0.264484i
$612$	−0.962976	−	4.19680i	−0.0389260	−	0.169645i
$613$	42.7632	+	11.4584i	1.72719	+	0.462799i	0.979532	−	0.201288i	$-0.0645126\pi$
$613$	42.7632	+	11.4584i	1.72719	+	0.462799i	0.747656	+	0.664086i	$0.231179\pi$
$614$	5.60681	+	2.04071i	0.226272	+	0.0823564i
$615$	−33.2350	−	15.1364i	−1.34016	−	0.610357i
$616$	3.53588	+	2.96695i	0.142464	+	0.119542i
$617$	5.99691	−	12.8604i	0.241427	−	0.517741i	−0.747837	−	0.663882i	$-0.768908\pi$
$617$	5.99691	−	12.8604i	0.241427	−	0.517741i	0.989264	+	0.146141i	$0.0466854\pi$
$618$	22.3362	−	1.54684i	0.898495	−	0.0622231i
$619$	21.7592	−	3.83673i	0.874576	−	0.154211i	0.281697	−	0.959503i	$-0.409103\pi$
$619$	21.7592	−	3.83673i	0.874576	−	0.154211i	0.592878	+	0.805292i	$0.297991\pi$
$620$	−1.14727	+	7.72473i	−0.0460753	+	0.310233i
$621$	0.533392	−	2.28934i	0.0214043	−	0.0918681i
$622$	5.47637	+	5.47637i	0.219582	+	0.219582i
$623$	−1.32127	+	1.88697i	−0.0529355	+	0.0755998i
$624$	−12.6843	+	4.35803i	−0.507778	+	0.174461i
$625$	−24.2793	−	5.95950i	−0.971172	−	0.238380i
$626$	−0.743054	+	0.885537i	−0.0296984	+	0.0353932i
$627$	33.3725	−	8.29691i	1.33277	−	0.331347i
$628$	25.6114	−	11.9428i	1.02201	−	0.476569i
$629$	−0.961899	−	1.66606i	−0.0383534	−	0.0664301i
$630$	6.03013	+	36.1300i	0.240246	+	1.43945i
$631$	6.92272	−	11.9905i	0.275589	−	0.477334i	−0.694694	−	0.719305i	$-0.744460\pi$
$631$	6.92272	−	11.9905i	0.275589	−	0.477334i	0.970284	+	0.241971i	$0.0777937\pi$
$632$	−0.161162	+	1.84210i	−0.00641070	+	0.0732746i
$633$	4.47520	+	0.473399i	0.177873	+	0.0188159i
$634$	22.9301	+	4.04320i	0.910672	+	0.160576i
$635$	2.87257	−	1.43548i	0.113994	−	0.0569654i
$636$	−4.87943	−	30.9418i	−0.193482	−	1.22692i
$637$	−0.444525	−	0.0388909i	−0.0176127	−	0.00154091i
$638$	100.208	−	26.8506i	3.96726	−	1.06302i
$639$	5.60293	−	4.36539i	0.221648	−	0.172692i
$640$	−1.92109	+	4.42925i	−0.0759377	+	0.175081i
$641$	−7.88689	+	21.6691i	−0.311513	+	0.855876i	0.680838	+	0.732434i	$0.261616\pi$
$641$	−7.88689	+	21.6691i	−0.311513	+	0.855876i	−0.992352	+	0.123442i	$0.960607\pi$
$642$	−26.6296	+	25.6814i	−1.05099	+	1.01356i
$643$	7.31553	−	0.640026i	0.288496	−	0.0252402i	0.0580110	−	0.998316i	$-0.481524\pi$
$643$	7.31553	−	0.640026i	0.288496	−	0.0252402i	0.230485	+	0.973076i	$0.425969\pi$
$644$	2.43549	−	0.886446i	0.0959718	−	0.0349309i
$645$	4.56424	−	12.8989i	0.179717	−	0.507894i
$646$	−0.742320	−	4.20990i	−0.0292062	−	0.165636i
$647$	−24.4108	+	24.4108i	−0.959686	+	0.959686i	−0.999218	−	0.0395324i	$-0.987413\pi$
$647$	−24.4108	+	24.4108i	−0.959686	+	0.959686i	0.0395324	+	0.999218i	$0.487413\pi$
$648$	−2.09004	+	1.24820i	−0.0821043	+	0.0490338i
$649$			50.4138i			1.97892i
$650$	21.0276	+	2.54293i	0.824769	+	0.0997418i
$651$	7.47615	+	1.45842i	0.293013	+	0.0571601i
$652$	−36.1497	−	16.8569i	−1.41573	−	0.660167i
$653$	−0.801061	−	9.15617i	−0.0313480	−	0.358309i	−0.995627	−	0.0934196i	$-0.970220\pi$
$653$	−0.801061	−	9.15617i	−0.0313480	−	0.358309i	0.964279	−	0.264889i	$-0.0853354\pi$
$654$	−0.174697	+	9.63778i	−0.00683118	+	0.376867i
$655$	−21.3274	+	39.3657i	−0.833329	+	1.53815i
$656$	−30.3465	+	17.5206i	−1.18483	+	0.684063i
$657$	−2.50419	+	3.31392i	−0.0976979	+	0.129288i
$658$	−8.86823	−	33.0967i	−0.345720	−	1.29024i
$659$	−23.2374	+	19.4985i	−0.905199	+	0.759552i	−0.971200	−	0.238267i	$-0.923421\pi$
$659$	−23.2374	+	19.4985i	−0.905199	+	0.759552i	0.0660005	+	0.997820i	$0.478976\pi$
$660$	−36.7794	+	37.4451i	−1.43164	+	1.45755i
$661$	1.43027	−	8.11147i	0.0556311	−	0.315500i	−0.944276	−	0.329156i	$-0.893236\pi$
$661$	1.43027	−	8.11147i	0.0556311	−	0.315500i	0.999907	+	0.0136561i	$0.00434700\pi$
$662$	−29.7872	−	42.5405i	−1.15771	−	1.65338i
$663$	−0.255466	+	2.41501i	−0.00992147	+	0.0937910i
$664$	0.688294	+	0.820277i	0.0267110	+	0.0318329i
$665$	2.14164	+	18.6457i	0.0830494	+	0.723050i
$666$	−11.6852	+	12.9427i	−0.452792	+	0.501521i
$667$	0.940421	−	3.50970i	0.0364132	−	0.135896i
$668$	6.79699	+	14.5762i	0.262984	+	0.563970i
$669$	−4.50723	+	7.48990i	−0.174260	+	0.289576i
$670$	16.1289	+	18.1969i	0.623112	+	0.703007i
$671$	−3.55969	−	9.78018i	−0.137420	−	0.377560i
$672$	33.8408	+	16.5334i	1.30544	+	0.637788i
$673$	−8.54498	−	5.98326i	−0.329385	−	0.230638i	0.397172	−	0.917744i	$-0.369992\pi$
$673$	−8.54498	−	5.98326i	−0.329385	−	0.230638i	−0.726557	+	0.687107i	$0.758881\pi$
$674$	−35.9537			−1.38488
$675$	−25.8823	+	2.25949i	−0.996211	+	0.0869679i
$676$	18.4683			0.710319
$677$	32.5175	+	22.7690i	1.24975	+	0.875083i	0.995748	−	0.0921212i	$-0.0293647\pi$
$677$	32.5175	+	22.7690i	1.24975	+	0.875083i	0.254000	+	0.967204i	$0.418254\pi$
$678$	−4.92692	−	71.1442i	−0.189217	−	2.73228i
$679$	−3.58382	−	9.84647i	−0.137535	−	0.377873i
$680$	0.269949	+	0.304562i	0.0103521	+	0.0116794i
$681$	−16.5793	−	29.9572i	−0.635319	−	1.14796i
$682$	8.93762	+	19.1668i	0.342239	+	0.733934i
$683$	0.244148	−	0.911173i	0.00934207	−	0.0348651i	−0.961097	−	0.276209i	$-0.910922\pi$
$683$	0.244148	−	0.911173i	0.00934207	−	0.0348651i	0.970440	+	0.241344i	$0.0775883\pi$
$684$	−17.6691	+	9.36443i	−0.675595	+	0.358058i
$685$	3.33567	+	29.0412i	0.127449	+	1.10961i
$686$	−23.8177	−	28.3848i	−0.909364	−	1.08374i
$687$	−39.5952	+	17.5971i	−1.51065	+	0.671371i
$688$	−7.53032	−	10.7544i	−0.287091	−	0.410008i
$689$	−3.06779	+	17.3983i	−0.116873	+	0.662822i
$690$	0.952719	+	3.43218i	0.0362694	+	0.130661i
$691$	−8.89879	+	7.46697i	−0.338526	+	0.284057i	−0.796163	−	0.605082i	$-0.793140\pi$
$691$	−8.89879	+	7.46697i	−0.338526	+	0.284057i	0.457637	+	0.889139i	$0.348696\pi$
$692$	4.14809	+	15.4809i	0.157687	+	0.588495i
$693$	34.8638	+	37.4876i	1.32437	+	1.42403i
$694$	−3.93170	+	2.26997i	−0.149245	+	0.0861668i
$695$	14.9457	−	27.5865i	0.566923	−	1.04642i
$696$	−3.29236	+	1.82210i	−0.124797	+	0.0690665i
$697$	0.552984	+	6.32063i	0.0209458	+	0.239411i
$698$	35.3665	+	16.4917i	1.33864	+	0.624219i
$699$	−9.30461	+	10.6892i	−0.351933	+	0.404304i
$700$	−17.6774	−	22.5411i	−0.668142	−	0.851974i
$701$		−	27.3341i		−	1.03240i	−0.856469	−	0.516198i	$-0.827347\pi$
$701$		−	27.3341i		−	1.03240i	0.856469	−	0.516198i	$-0.172653\pi$
$702$	21.5399	−	4.53314i	0.812969	−	0.171092i
$703$	−6.31764	+	6.31764i	−0.238274	+	0.238274i
$704$	9.95862	+	56.4781i	0.375330	+	2.12860i
$705$	23.8949	−	4.43462i	0.899934	−	0.167018i
$706$	−56.7662	+	20.6612i	−2.13643	+	0.777595i
$707$	36.4794	−	3.19154i	1.37195	−	0.120030i
$708$	−7.07315	−	28.4502i	−0.265825	−	1.06922i
$709$	10.1733	−	27.9510i	0.382068	−	1.04972i	−0.588417	−	0.808558i	$-0.700249\pi$
$709$	10.1733	−	27.9510i	0.382068	−	1.04972i	0.970484	−	0.241164i	$-0.0775292\pi$
$710$	−4.28267	+	9.87409i	−0.160726	+	0.370568i
$711$	−4.29095	+	20.0550i	−0.160923	+	0.752120i
$712$	0.224078	−	0.0600414i	0.00839766	−	0.00225015i
$713$	0.737882	+	0.0645563i	0.0276339	+	0.00241765i
$714$	4.94840	−	4.00164i	0.185189	−	0.149758i
$715$	26.4800	−	13.2326i	0.990296	−	0.494872i
$716$	27.1382	+	4.78519i	1.01420	+	0.178831i
$717$	−16.3513	+	22.4739i	−0.610650	+	0.839303i
$718$	4.99610	−	57.1057i	0.186453	−	2.13116i
$719$	4.04581	−	7.00756i	0.150883	−	0.261338i	−0.780669	−	0.624945i	$-0.785122\pi$
$719$	4.04581	−	7.00756i	0.150883	−	0.261338i	0.931552	+	0.363607i	$0.118455\pi$
$720$	−12.6617	+	21.4741i	−0.471872	+	0.800294i
$721$	8.53917	+	14.7903i	0.318015	+	0.550819i
$722$	17.0147	−	7.93406i	0.633220	−	0.295275i
$723$	−13.8586	−	14.3703i	−0.515407	−	0.534437i
$724$	7.24389	−	8.63293i	0.269217	−	0.320840i
$725$	−40.1006	+	2.17495i	−1.48930	+	0.0807756i
$726$	−19.7981	+	101.489i	−0.734776	+	3.76660i
$727$	−26.0879	+	37.2574i	−0.967546	+	1.38180i	−0.0436958	+	0.999045i	$0.513913\pi$
$727$	−26.0879	+	37.2574i	−0.967546	+	1.38180i	−0.923850	+	0.382754i	$0.874976\pi$
$728$	1.07044	+	1.07044i	0.0396730	+	0.0396730i
$729$	−24.7097	+	10.8825i	−0.915175	+	0.403056i
$730$	0.924644	−	6.22578i	0.0342226	−	0.230427i
$731$	−2.34106	+	0.412792i	−0.0865872	+	0.0152677i
$732$	3.38103	+	5.01984i	0.124966	+	0.185539i
$733$	11.4484	−	24.5512i	0.422857	−	0.906819i	−0.573309	−	0.819339i	$-0.694341\pi$
$733$	11.4484	−	24.5512i	0.422857	−	0.906819i	0.996166	−	0.0874805i	$-0.0278815\pi$
$734$	−37.4655	−	31.4373i	−1.38288	−	1.16037i
$735$	−0.675106	+	0.481794i	−0.0249017	+	0.0177713i
$736$	3.44161	+	1.25265i	0.126860	+	0.0461731i
$737$	32.8260	+	8.79571i	1.20916	+	0.323994i
$738$	52.9674	−	22.3995i	1.94976	−	0.824536i
$739$	−13.2893	−	7.67257i	−0.488854	−	0.282240i	0.235245	−	0.971936i	$-0.424411\pi$
$739$	−13.2893	−	7.67257i	−0.488854	−	0.282240i	−0.724099	+	0.689696i	$0.757744\pi$
$740$	3.17131	−	13.2628i	0.116580	−	0.487549i
$741$	11.1407	−	1.75684i	0.409262	−	0.0645393i
$742$	37.9237	−	26.5545i	1.39222	−	0.974846i
$743$	31.3637	−	21.9611i	1.15062	−	0.805674i	0.167007	−	0.985956i	$-0.446590\pi$
$743$	31.3637	−	21.9611i	1.15062	−	0.805674i	0.983615	+	0.180282i	$0.0577010\pi$
$744$	−0.482342	−	0.596460i	−0.0176835	−	0.0218673i
$745$	−2.18629	+	1.34251i	−0.0800995	+	0.0491856i
$746$	−12.6415	−	7.29858i	−0.462839	−	0.267220i
$747$	6.45491	+	9.96896i	0.236173	+	0.364745i
$748$	8.80816	+	2.36014i	0.322058	+	0.0862953i
$749$	−26.5175	−	9.65157i	−0.968927	−	0.352661i
$750$	32.7840	−	21.7968i	1.19710	−	0.795907i
$751$	−6.83954	−	5.73906i	−0.249578	−	0.209421i	0.509412	−	0.860523i	$-0.329863\pi$
$751$	−6.83954	−	5.73906i	−0.249578	−	0.209421i	−0.758991	+	0.651101i	$0.774307\pi$
$752$	9.85508	−	21.1343i	0.359378	−	0.770688i
$753$	−0.457569	+	0.936559i	−0.0166747	+	0.0341301i
$754$	33.5075	−	5.90827i	1.22027	−	0.215167i
$755$	−3.48812	−	0.518050i	−0.126946	−	0.0188538i
$756$	−24.9343	−	16.2640i	−0.906853	−	0.591516i
$757$	−12.0849	−	12.0849i	−0.439232	−	0.439232i	0.452522	−	0.891753i	$-0.350525\pi$
$757$	−12.0849	−	12.0849i	−0.439232	−	0.439232i	−0.891753	+	0.452522i	$0.850525\pi$
$758$	−7.70890	+	11.0094i	−0.280000	+	0.399881i
$759$	3.75489	+	3.26850i	0.136294	+	0.118639i
$760$	1.04177	−	1.57706i	0.0377889	−	0.0572060i
$761$	−28.7638	+	34.2794i	−1.04269	+	1.24263i	−0.0732447	+	0.997314i	$0.523335\pi$
$761$	−28.7638	+	34.2794i	−1.04269	+	1.24263i	−0.969444	+	0.245314i	$0.921109\pi$
$762$	−1.39714	+	4.86010i	−0.0506131	+	0.176063i
$763$	−6.66378	+	3.10737i	−0.241245	+	0.112494i
$764$	19.8465	+	34.3752i	0.718022	+	1.24365i
$765$	2.55505	+	3.72105i	0.0923782	+	0.134535i
$766$	9.94557	−	17.2262i	0.359348	−	0.622409i
$767$	−1.44105	+	16.4713i	−0.0520333	+	0.594743i
$768$	9.61149	+	21.6268i	0.346825	+	0.780390i
$769$	22.4692	+	3.96193i	0.810262	+	0.142871i	0.563405	−	0.826181i	$-0.309491\pi$
$769$	22.4692	+	3.96193i	0.810262	+	0.142871i	0.246857	+	0.969052i	$0.420602\pi$
$770$	−73.5877	−	24.5475i	−2.65191	−	0.884629i
$771$	14.2561	+	5.48338i	0.513421	+	0.197479i
$772$	−12.1954	−	1.06696i	−0.438921	−	0.0384006i
$773$	−40.1817	+	10.7667i	−1.44524	+	0.387250i	−0.894364	−	0.447339i	$-0.852372\pi$
$773$	−40.1817	+	10.7667i	−1.44524	+	0.387250i	−0.550872	+	0.834589i	$0.685705\pi$
$774$	10.0900	+	19.0381i	0.362678	+	0.684311i
$775$	−1.85614	−	7.97343i	−0.0666745	−	0.286414i
$776$	−0.360912	+	0.991598i	−0.0129560	+	0.0355963i
$777$	−12.7830	−	3.67475i	−0.458588	−	0.131831i
$778$	−19.7522	+	1.72809i	−0.708149	+	0.0619550i
$779$	27.6893	−	10.0781i	0.992074	−	0.361085i
$780$	−13.0870	+	11.1828i	−0.468588	+	0.400408i
$781$	2.61204	+	14.8136i	0.0934662	+	0.530073i
$782$	0.437588	−	0.437588i	0.0156481	−	0.0156481i
$783$	−38.7274	+	15.5563i	−1.38401	+	0.555936i
$784$			0.795819i			0.0284221i
$785$	−20.3721	+	21.5070i	−0.727112	+	0.767617i
$786$	−22.9092	−	66.6785i	−0.817145	−	2.37834i
$787$	−0.509559	−	0.237611i	−0.0181638	−	0.00846992i	0.413515	−	0.910497i	$-0.364301\pi$
$787$	−0.509559	−	0.237611i	−0.0181638	−	0.00846992i	−0.431679	+	0.902027i	$0.642079\pi$
$788$	3.16416	+	36.1666i	0.112719	+	1.28838i
$789$	−17.7482	−	10.6804i	−0.631854	−	0.380234i
$790$	−8.85356	−	29.7893i	−0.314995	−	1.05986i
$791$	47.1092	−	27.1985i	1.67501	−	0.967068i
$792$	−0.262909	−	5.14880i	−0.00934208	−	0.182955i
$793$	−0.883467	−	3.29714i	−0.0313728	−	0.117085i
$794$	35.3263	−	29.6423i	1.25368	−	1.05197i
$795$	16.6729	+	28.2894i	0.591327	+	1.00332i
$796$	8.58929	−	48.7123i	0.304439	−	1.72656i
$797$	29.3985	+	41.9854i	1.04135	+	1.48720i	0.864288	+	0.502998i	$0.167770\pi$
$797$	29.3985	+	41.9854i	1.04135	+	1.48720i	0.177060	+	0.984200i	$0.443341\pi$
$798$	−23.8991	−	17.3882i	−0.846020	−	0.615537i
$799$	−2.71405	−	3.23448i	−0.0960162	−	0.114428i
$800$	1.33892	−	40.4577i	0.0473379	−	1.43040i
$801$	2.54837	−	0.354664i	0.0900423	−	0.0125314i
$802$	16.5253	−	61.6733i	0.583529	−	2.17776i
$803$	−3.71760	−	7.97242i	−0.131191	−	0.281341i
$804$	−19.7589	−	0.358154i	−0.696841	−	0.0126311i
$805$	−2.03325	+	1.80217i	−0.0716626	+	0.0635183i
$806$	2.37224	+	6.51767i	0.0835585	+	0.229575i
$807$	22.5131	−	15.1633i	0.792497	−	0.533773i
$808$	−3.02081	−	2.11519i	−0.106272	−	0.0744122i
$809$	10.4010			0.365681			0.182841	−	0.983143i	$-0.441471\pi$
$809$	10.4010			0.365681			0.182841	+	0.983143i	$0.441471\pi$
$810$	24.9638	−	32.4144i	0.877139	−	1.13893i
$811$	3.01122			0.105738			0.0528692	−	0.998601i	$-0.483163\pi$
$811$	3.01122			0.105738			0.0528692	+	0.998601i	$0.483163\pi$
$812$	−37.6944	−	26.3939i	−1.32281	−	0.926244i
$813$	−22.0578	+	14.8567i	−0.773602	+	0.521046i
$814$	−12.6302	−	34.7013i	−0.442690	−	1.21628i
$815$	41.7375	+	2.51456i	1.46200	+	0.0880813i
$816$	4.33038	+	0.0784935i	0.151594	+	0.00274782i
$817$	4.66573	+	10.0057i	0.163233	+	0.350055i
$818$	−15.0316	+	56.0987i	−0.525568	+	1.96145i
$819$	10.3192	+	13.2445i	0.360581	+	0.462802i
$820$	−27.9651	+	35.2228i	−0.976582	+	1.23003i
$821$	23.3489	+	27.8262i	0.814883	+	0.971140i	0.999933	−	0.0115894i	$-0.00368910\pi$
$821$	23.3489	+	27.8262i	0.814883	+	0.971140i	−0.185050	+	0.982729i	$0.559245\pi$
$822$	−37.2235	−	27.0826i	−1.29832	−	0.944616i
$823$	−4.70013	−	6.71249i	−0.163836	−	0.233983i	0.728836	−	0.684688i	$-0.240061\pi$
$823$	−4.70013	−	6.71249i	−0.163836	−	0.233983i	−0.892673	+	0.450705i	$0.851173\pi$
$824$	0.298656	−	1.69376i	0.0104042	−	0.0590049i
$825$	21.4402	−	50.6725i	0.746454	−	1.76419i
$826$	33.1916	−	27.8511i	1.15488	−	0.969063i
$827$	2.16528	+	8.08092i	0.0752940	+	0.281001i	0.993300	−	0.115566i	$-0.0368681\pi$
$827$	2.16528	+	8.08092i	0.0752940	+	0.281001i	−0.918006	+	0.396567i	$0.870201\pi$
$828$	−2.57758	−	1.31770i	−0.0895772	−	0.0457934i
$829$	−24.2355	+	13.9924i	−0.841734	+	0.485975i	−0.857853	−	0.513895i	$-0.828202\pi$
$829$	−24.2355	+	13.9924i	−0.841734	+	0.485975i	0.0161192	+	0.999870i	$0.494869\pi$
$830$	−15.8231	−	8.57259i	−0.549229	−	0.297559i
$831$	−6.42961	−	3.86918i	−0.223041	−	0.134220i
$832$	1.63930	+	18.7373i	0.0568325	+	0.649598i
$833$	0.130596	+	0.0608977i	0.00452487	+	0.00210998i
$834$	16.0542	+	46.7267i	0.555913	+	1.61801i
$835$	−12.2403	−	11.5944i	−0.423592	−	0.401240i
$836$		−	42.3499i		−	1.46470i
$837$	−4.49391	−	7.22408i	−0.155332	−	0.249701i
$838$	−5.83376	+	5.83376i	−0.201524	+	0.201524i
$839$	4.76834	+	27.0426i	0.164621	+	0.933615i	0.949454	+	0.313907i	$0.101638\pi$
$839$	4.76834	+	27.0426i	0.164621	+	0.933615i	−0.784832	+	0.619708i	$0.787251\pi$
$840$	2.80513	+	0.220088i	0.0967862	+	0.00759374i
$841$	−33.3699	+	12.1457i	−1.15069	+	0.418816i
$842$	19.8966	−	1.74073i	0.685683	−	0.0599895i
$843$	29.6279	+	8.51718i	1.02044	+	0.293347i
$844$	1.89549	−	5.20781i	0.0652454	−	0.179260i
$845$	−18.0066	+	7.11199i	−0.619448	+	0.244660i
$846$	−20.3241	+	32.4284i	−0.698756	+	1.11491i
$847$	−76.1848	+	20.4137i	−2.61774	+	0.701421i
$848$	31.3879	+	2.74608i	1.07786	+	0.0943009i
$849$	32.0872	+	12.3418i	1.10123	+	0.423570i
$850$	−6.09995	−	3.09408i	−0.209227	−	0.106126i
$851$	−1.27374	−	0.224595i	−0.0436632	−	0.00769900i
$852$	−3.55244	−	7.99334i	−0.121705	−	0.273847i
$853$	1.45086	−	16.5834i	0.0496766	−	0.567806i	−0.930045	−	0.367444i	$-0.880233\pi$
$853$	1.45086	−	16.5834i	0.0496766	−	0.567806i	0.979722	−	0.200361i	$-0.0642116\pi$
$854$	−4.47255	+	7.74669i	−0.153048	+	0.265086i
$855$	13.6213	−	15.9346i	0.465837	−	0.544951i
$856$	1.42092	+	2.46111i	0.0485662	+	0.0841191i
$857$	9.84971	−	4.59299i	0.336460	−	0.156894i	−0.247044	−	0.969004i	$-0.579459\pi$
$857$	9.84971	−	4.59299i	0.336460	−	0.156894i	0.583504	+	0.812111i	$0.301681\pi$
$858$	−12.8792	+	44.8016i	−0.439688	+	1.52950i
$859$	0.275808	−	0.328695i	0.00941045	−	0.0112149i	−0.761319	−	0.648378i	$-0.775448\pi$
$859$	0.275808	−	0.328695i	0.00941045	−	0.0112149i	0.770729	+	0.637163i	$0.219892\pi$
$860$	−14.0598	−	9.28752i	−0.479434	−	0.316702i
$861$	33.0871	+	28.8012i	1.12760	+	0.981541i
$862$	−4.17115	+	5.95703i	−0.142070	+	0.202897i
$863$	−7.52083	−	7.52083i	−0.256012	−	0.256012i	0.567418	−	0.823430i	$-0.307942\pi$
$863$	−7.52083	−	7.52083i	−0.256012	−	0.256012i	−0.823430	+	0.567418i	$0.807942\pi$
$864$	−12.2185	−	40.2544i	−0.415681	−	1.36948i
$865$	−10.0060	−	13.4965i	−0.340213	−	0.458895i
$866$	−1.90056	+	0.335120i	−0.0645837	+	0.0113878i
$867$	−12.5813	+	25.7516i	−0.427283	+	0.874570i
$868$	3.96439	−	8.50167i	0.134560	−	0.288565i
$869$	−33.2719	−	27.9184i	−1.12867	−	0.947068i
$870$	40.2145	−	48.8081i	1.36340	−	1.65475i
$871$	10.4735	+	3.81206i	0.354883	+	0.129167i
$872$	0.715226	+	0.191644i	0.0242206	+	0.00648989i
$873$	−5.32736	+	10.4209i	−0.180304	+	0.352696i
$874$	−2.48898	−	1.43701i	−0.0841909	−	0.0486077i
$875$	25.9159	+	15.1702i	0.876116	+	0.512848i
$876$	3.21651	+	3.97751i	0.108676	+	0.134388i
$877$	4.01504	−	2.81136i	0.135578	−	0.0949330i	−0.503820	−	0.863809i	$-0.668072\pi$
$877$	4.01504	−	2.81136i	0.135578	−	0.0949330i	0.639398	+	0.768876i	$0.279184\pi$
$878$	−54.7890	+	38.3637i	−1.84904	+	1.29471i
$879$	28.1516	−	4.43942i	0.949530	−	0.149738i
$880$	−27.6260	−	44.9894i	−0.931273	−	1.51659i
$881$	−0.734747	−	0.424206i	−0.0247542	−	0.0142919i	0.487572	−	0.873083i	$-0.337883\pi$
$881$	−0.734747	−	0.424206i	−0.0247542	−	0.0142919i	−0.512326	+	0.858791i	$0.671216\pi$
$882$	0.160911	−	1.29614i	0.00541817	−	0.0436432i
$883$	33.9530	+	9.09767i	1.14261	+	0.306161i	0.779999	−	0.625781i	$-0.215219\pi$
$883$	33.9530	+	9.09767i	1.14261	+	0.306161i	0.362609	+	0.931941i	$0.381886\pi$
$884$	2.81035	+	1.02288i	0.0945223	+	0.0344033i
$885$	17.8523	+	25.0152i	0.600097	+	0.840876i
$886$	34.9135	+	29.2959i	1.17294	+	0.984216i
$887$	9.41211	−	20.1843i	0.316028	−	0.677724i	−0.682561	−	0.730828i	$-0.739134\pi$
$887$	9.41211	−	20.1843i	0.316028	−	0.677724i	0.998589	+	0.0531048i	$0.0169117\pi$
$888$	0.748271	+	1.11096i	0.0251103	+	0.0372815i
$889$	−3.79871	+	0.669814i	−0.127405	+	0.0224649i
$890$	−3.13194	+	2.32194i	−0.104983	+	0.0778314i
$891$	4.14177	−	57.0300i	0.138754	−	1.91058i
$892$	7.61222	+	7.61222i	0.254876	+	0.254876i
$893$	−11.2474	+	16.0630i	−0.376380	+	0.537526i
$894$	0.773556	−	3.96539i	0.0258716	−	0.132623i
$895$	−28.3025	+	5.78510i	−0.946049	+	0.193375i
$896$	3.72765	−	4.44244i	0.124532	−	0.148412i
$897$	1.13337	+	1.17522i	0.0378423	+	0.0392395i
$898$	−18.2878	+	8.52775i	−0.610272	+	0.284575i
$899$	−6.57542	−	11.3890i	−0.219303	−	0.379843i
$900$	−4.98999	+	31.6042i	−0.166333	+	1.05347i
$901$	2.85250	−	4.94068i	0.0950307	−	0.164598i
$902$	−10.6148	+	121.328i	−0.353435	+	4.03979i
$903$	−9.66932	+	13.2899i	−0.321775	+	0.442261i
$904$	−5.39488	−	0.951262i	−0.179431	−	0.0316385i
$905$	−3.73834	+	11.2067i	−0.124267	+	0.372523i
$906$	4.31796	−	3.49182i	0.143454	−	0.116008i
$907$	50.6679	+	4.43286i	1.68240	+	0.147191i	0.887888	−	0.460060i	$-0.152172\pi$
$907$	50.6679	+	4.43286i	1.68240	+	0.147191i	0.794511	+	0.607250i	$0.207727\pi$
$908$	−40.7291	+	10.9133i	−1.35164	+	0.362171i
$909$	−30.3585	−	27.4088i	−1.00693	−	0.909092i
$910$	−23.3410	−	10.1236i	−0.773746	−	0.335595i
$911$	−1.01302	+	2.78325i	−0.0335629	+	0.0922132i	−0.955342	−	0.295502i	$-0.904513\pi$
$911$	−1.01302	+	2.78325i	−0.0335629	+	0.0922132i	0.921779	+	0.387715i	$0.126735\pi$
$912$	−4.85302	−	19.5202i	−0.160700	−	0.646378i
$913$	−25.0557	+	2.19209i	−0.829223	+	0.0725476i
$914$	−66.0043	+	24.0236i	−2.18323	+	0.794630i
$915$	−5.22961	−	3.59235i	−0.172885	−	0.118760i
$916$	9.26601	+	52.5502i	0.306158	+	1.73631i
$917$	38.0275	−	38.0275i	1.25578	−	1.25578i
$918$	−7.03694	−	1.00343i	−0.232254	−	0.0331180i
$919$		−	4.33194i		−	0.142897i	−0.997444	−	0.0714487i	$-0.977238\pi$
$919$		−	4.33194i		−	0.142897i	0.997444	−	0.0714487i	$-0.0227622\pi$
$920$	0.273514	−	0.00741190i	0.00901750	−	0.000244363i
$921$	3.33759	−	3.83426i	0.109977	−	0.126343i
$922$	19.2436	+	8.97345i	0.633755	+	0.295525i
$923$	0.429971	+	4.91459i	0.0141527	+	0.161766i
$924$	55.1617	−	30.5283i	1.81469	−	1.00431i
$925$	2.01534	+	14.1525i	0.0662639	+	0.465331i
$926$	32.5250	−	18.7783i	1.06884	−	0.617093i
$927$	5.60159	−	18.2344i	0.183980	−	0.598897i
$928$	−16.8300	−	62.8104i	−0.552472	−	2.06185i
$929$	−24.5535	+	20.6028i	−0.805574	+	0.675957i	−0.949547	−	0.313625i	$-0.898457\pi$
$929$	−24.5535	+	20.6028i	−0.805574	+	0.675957i	0.143973	+	0.989582i	$0.454012\pi$
$930$	11.2220	+	6.34556i	0.367985	+	0.208079i
$931$	0.116207	−	0.659044i	0.00380854	−	0.0215993i
$932$	10.0104	+	14.2963i	0.327902	+	0.468292i
$933$	6.02966	−	2.67973i	0.197402	−	0.0877304i
$934$	50.3203	+	59.9694i	1.64653	+	1.96226i
$935$	−9.49685	+	1.09081i	−0.310580	+	0.0356732i
$936$	0.0612774	−	1.68974i	0.00200291	−	0.0552308i
$937$	−3.81043	+	14.2207i	−0.124481	+	0.464571i	−0.999821	−	0.0189383i	$-0.993971\pi$
$937$	−3.81043	+	14.2207i	−0.124481	+	0.464571i	0.875339	+	0.483509i	$0.160638\pi$
$938$	−12.3438	−	26.4713i	−0.403038	−	0.864318i
$939$	0.476896	+	0.861705i	0.0155629	+	0.0281207i
$940$	1.79990	−	29.8753i	0.0587062	−	0.974425i
$941$	−0.647073	−	1.77782i	−0.0210940	−	0.0579552i	0.928699	−	0.370835i	$-0.120928\pi$
$941$	−0.647073	−	1.77782i	−0.0210940	−	0.0579552i	−0.949793	+	0.312880i	$0.898706\pi$
$942$	−3.22292	−	46.5386i	−0.105008	−	1.51631i
$943$	3.49422	+	2.44668i	0.113788	+	0.0796749i
$944$	29.4880			0.959753
$945$	30.5742	+	6.25544i	0.994578	+	0.203489i
$946$	−45.6312			−1.48360
$947$	−27.3760	−	19.1689i	−0.889601	−	0.622906i	0.0368497	−	0.999321i	$-0.488268\pi$
$947$	−27.3760	−	19.1689i	−0.889601	−	0.622906i	−0.926451	+	0.376415i	$0.877157\pi$
$948$	22.6934	+	11.0872i	0.737048	+	0.360095i
$949$	−0.986732	−	2.71103i	−0.0320307	−	0.0880036i
$950$	−6.54768	+	31.0832i	−0.212435	+	1.00847i
$951$	10.2283	−	16.9969i	0.331676	−	0.551164i
$952$	−0.206598	−	0.443050i	−0.00669587	−	0.0143593i
$953$	4.71015	−	17.5785i	0.152577	−	0.569424i	−0.846724	−	0.532032i	$-0.821428\pi$
$953$	4.71015	−	17.5785i	0.152577	−	0.569424i	0.999301	−	0.0373915i	$-0.0119049\pi$
$954$	−50.5656	−	10.8190i	−1.63712	−	0.350278i
$955$	−32.5880	−	25.8732i	−1.05452	−	0.837236i
$956$	22.0009	+	26.2197i	0.711560	+	0.848004i
$957$	9.29781	−	87.8954i	0.300555	−	2.84125i
$958$	−17.1557	−	24.5009i	−0.554275	−	0.791587i
$959$	6.09731	−	34.5796i	0.196893	−	1.11663i
$960$	24.9411	+	24.4978i	0.804972	+	0.790662i
$961$	−21.6937	+	18.2032i	−0.699798	+	0.587200i
$962$	−3.13465	−	11.6987i	−0.101065	−	0.377181i
$963$	12.2766	+	29.0301i	0.395607	+	0.935481i
$964$	−21.2922	+	12.2931i	−0.685777	+	0.395934i
$965$	12.3014	−	3.65605i	0.395996	−	0.117692i
$966$	0.0775412	−	4.27784i	0.00249485	−	0.137637i
$967$	3.69964	+	42.2870i	0.118972	+	1.35986i	0.787566	+	0.616231i	$0.211341\pi$
$967$	3.69964	+	42.2870i	0.118972	+	1.35986i	−0.668593	+	0.743628i	$0.733103\pi$
$968$	7.19871	+	3.35682i	0.231375	+	0.107892i
$969$	−3.57467	−	0.697335i	−0.114835	−	0.0224016i
$970$	−0.480411	−	17.7281i	−0.0154251	−	0.569216i
$971$		−	8.10739i		−	0.260179i	−0.991502	−	0.130089i	$-0.958474\pi$
$971$		−	8.10739i		−	0.260179i	0.991502	−	0.130089i	$-0.0415264\pi$
$972$	5.66408	+	32.7650i	0.181675	+	1.05094i
$973$	−26.6487	+	26.6487i	−0.854319	+	0.854319i
$974$	−1.70235	−	9.65451i	−0.0545468	−	0.309350i
$975$	8.45343	−	15.9429i	0.270726	−	0.510582i
$976$	−5.72061	+	2.08213i	−0.183112	+	0.0666475i
$977$	−42.0388	+	3.67792i	−1.34494	+	0.117667i	−0.736772	−	0.676141i	$-0.763651\pi$
$977$	−42.0388	+	3.67792i	−1.34494	+	0.117667i	−0.608168	+	0.793808i	$0.708095\pi$
$978$	−47.3958	+	45.7081i	−1.51555	+	1.46159i
$979$	−1.86364	+	5.12031i	−0.0595622	+	0.163646i
$980$	0.375216	+	0.949998i	0.0119858	+	0.0303466i
$981$	7.61033	+	3.08666i	0.242979	+	0.0985495i
$982$	12.6966	−	3.40203i	0.405163	−	0.108563i
$983$	14.2769	+	1.24906i	0.455362	+	0.0398390i	0.312530	−	0.949908i	$-0.398824\pi$
$983$	14.2769	+	1.24906i	0.455362	+	0.0398390i	0.142832	+	0.989747i	$0.454379\pi$
$984$	−0.688138	−	4.36368i	−0.0219370	−	0.139109i
$985$	−17.0125	−	34.0440i	−0.542064	−	1.08473i
$986$	−10.8204	−	1.90793i	−0.344592	−	0.0607608i
$987$	−29.0302	−	3.07089i	−0.924041	−	0.0977475i
$988$	1.21055	−	13.8366i	0.0385126	−	0.440201i
$989$	−0.799099	+	1.38408i	−0.0254099	+	0.0440112i
$990$	35.8973	+	78.8592i	1.14089	+	2.50631i
$991$	15.7989	+	27.3646i	0.501870	+	0.869265i	0.999998	+	0.00216080i	$0.000687805\pi$
$991$	15.7989	+	27.3646i	0.501870	+	0.869265i	−0.498128	+	0.867104i	$0.665979\pi$
$992$	12.0138	−	5.60212i	0.381438	−	0.177867i
$993$	−42.9379	+	10.6750i	−1.36259	+	0.338761i
$994$	8.31002	−	9.90350i	0.263578	−	0.314120i
$995$	10.3841	+	50.8023i	0.329198	+	1.61054i
$996$	13.8322	−	4.75243i	0.438290	−	0.150586i
$997$	7.09629	−	10.1346i	0.224742	−	0.320965i	−0.690907	−	0.722944i	$-0.742789\pi$
$997$	7.09629	−	10.1346i	0.224742	−	0.320965i	0.915649	+	0.401979i	$0.131678\pi$
$998$	36.2043	+	36.2043i	1.14603	+	1.14603i
$999$	6.71785	+	13.2504i	0.212543	+	0.419224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.122.3	yes	192
3.2	odd	2		405.2.r.a.152.14		192
5.2	odd	4		675.2.ba.b.68.14		192
5.3	odd	4	inner	135.2.q.a.68.3	yes	192
5.4	even	2		675.2.ba.b.257.14		192
15.8	even	4		405.2.r.a.233.14		192
27.2	odd	18	inner	135.2.q.a.2.3	✓	192
27.25	even	9		405.2.r.a.332.14		192
135.2	even	36		675.2.ba.b.218.14		192
135.29	odd	18		675.2.ba.b.407.14		192
135.83	even	36	inner	135.2.q.a.83.3	yes	192
135.133	odd	36		405.2.r.a.8.14		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.3	✓	192	27.2	odd	18	inner
135.2.q.a.68.3	yes	192	5.3	odd	4	inner
135.2.q.a.83.3	yes	192	135.83	even	36	inner
135.2.q.a.122.3	yes	192	1.1	even	1	trivial
405.2.r.a.8.14		192	135.133	odd	36
405.2.r.a.152.14		192	3.2	odd	2
405.2.r.a.233.14		192	15.8	even	4
405.2.r.a.332.14		192	27.25	even	9
675.2.ba.b.68.14		192	5.2	odd	4
675.2.ba.b.218.14		192	135.2	even	36
675.2.ba.b.257.14		192	5.4	even	2
675.2.ba.b.407.14		192	135.29	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66533 - 1.16608i) q^{2} +(-1.43658 + 0.967587i) q^{3} +(0.729546 + 2.00441i) q^{4} +(-1.48319 - 1.67336i) q^{5} +(3.52066 + 0.0638164i) q^{6} +(1.13512 + 2.43427i) q^{7} +(0.0700073 - 0.261271i) q^{8} +(1.12755 - 2.78004i) q^{9} +O(q^{10})\)	\(q+(-1.66533 - 1.16608i) q^{2} +(-1.43658 + 0.967587i) q^{3} +(0.729546 + 2.00441i) q^{4} +(-1.48319 - 1.67336i) q^{5} +(3.52066 + 0.0638164i) q^{6} +(1.13512 + 2.43427i) q^{7} +(0.0700073 - 0.261271i) q^{8} +(1.12755 - 2.78004i) q^{9} +(0.518731 + 4.51621i) q^{10} +(4.08386 + 4.86695i) q^{11} +(-2.98750 - 2.17361i) q^{12} +(1.19516 + 1.70687i) q^{13} +(0.948196 - 5.37749i) q^{14} +(3.74985 + 0.968813i) q^{15} +(2.84677 - 2.38873i) q^{16} +(-0.174154 - 0.649952i) q^{17} +(-5.11948 + 3.31487i) q^{18} +(-2.70632 + 1.56249i) q^{19} +(2.27205 - 4.19372i) q^{20} +(-3.98606 - 2.39871i) q^{21} +(-1.12573 - 12.8672i) q^{22} +(-0.409999 - 0.191186i) q^{23} +(0.152231 + 0.443076i) q^{24} +(-0.600292 + 4.96383i) q^{25} -4.23615i q^{26} +(1.07011 + 5.08477i) q^{27} +(-4.05115 + 4.05115i) q^{28} +(1.39473 + 7.90988i) q^{29} +(-5.11503 - 5.98600i) q^{30} +(-1.53858 + 0.559998i) q^{31} +(-8.06517 + 0.705611i) q^{32} +(-10.5760 - 3.04030i) q^{33} +(-0.467869 + 1.28546i) q^{34} +(2.38982 - 5.50995i) q^{35} +(6.39494 + 0.231909i) q^{36} +(2.76163 - 0.739977i) q^{37} +(6.32889 + 0.553706i) q^{38} +(-3.36850 - 1.29564i) q^{39} +(-0.541035 + 0.270367i) q^{40} +(-9.28604 - 1.63738i) q^{41} +(3.84102 + 8.64268i) q^{42} +(0.307907 - 3.51939i) q^{43} +(-6.77601 + 11.7364i) q^{44} +(-6.32439 + 2.23653i) q^{45} +(0.459846 + 0.796477i) q^{46} +(5.68707 - 2.65193i) q^{47} +(-1.77833 + 6.18611i) q^{48} +(-0.137652 + 0.164047i) q^{49} +(6.78789 - 7.56643i) q^{50} +(0.879072 + 0.765202i) q^{51} +(-2.54934 + 3.64084i) q^{52} +(5.99520 + 5.99520i) q^{53} +(4.14714 - 9.71563i) q^{54} +(2.08704 - 14.0524i) q^{55} +(0.715470 - 0.126157i) q^{56} +(2.37601 - 4.86325i) q^{57} +(6.90084 - 14.7989i) q^{58} +(6.07856 + 5.10051i) q^{59} +(0.793791 + 8.22304i) q^{60} +(-1.53937 - 0.560286i) q^{61} +(3.21525 + 0.861522i) q^{62} +(8.04727 - 0.410911i) q^{63} +(7.81729 + 4.51332i) q^{64} +(1.08356 - 4.53156i) q^{65} +(14.0673 + 17.3955i) q^{66} +(4.38163 - 3.06805i) q^{67} +(1.17572 - 0.823246i) q^{68} +(0.773987 - 0.122055i) q^{69} +(-10.4048 + 6.38916i) q^{70} +(2.05039 + 1.18380i) q^{71} +(-0.647407 - 0.489220i) q^{72} +(-1.33738 - 0.358350i) q^{73} +(-5.46189 - 1.98796i) q^{74} +(-3.94057 - 7.71180i) q^{75} +(-5.10626 - 4.28466i) q^{76} +(-7.21181 + 15.4658i) q^{77} +(4.09885 + 6.08559i) q^{78} +(-6.73243 + 1.18711i) q^{79} +(-8.21952 - 1.22075i) q^{80} +(-6.45726 - 6.26928i) q^{81} +(13.5550 + 13.5550i) q^{82} +(-2.27065 + 3.24283i) q^{83} +(1.89998 - 9.73966i) q^{84} +(-0.829302 + 1.25543i) q^{85} +(-4.61664 + 5.50190i) q^{86} +(-9.65714 - 10.0137i) q^{87} +(1.55749 - 0.726271i) q^{88} +(0.428822 + 0.742742i) q^{89} +(13.1401 + 3.65017i) q^{90} +(-2.79833 + 4.84685i) q^{91} +(0.0841016 - 0.961286i) q^{92} +(1.66846 - 2.29320i) q^{93} +(-12.5632 - 2.21523i) q^{94} +(6.62860 + 2.21118i) q^{95} +(10.9036 - 8.81742i) q^{96} +(-3.88639 - 0.340015i) q^{97} +(0.420527 - 0.112680i) q^{98} +(18.1351 - 5.86555i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

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